import pandas as pd

# Cargando los datos
df = pd.read_csv('../data/raw/life_expectancy_data.csv')
df

df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 2938 entries, 0 to 2937
Data columns (total 22 columns):
 #   Column                           Non-Null Count  Dtype  
---  ------                           --------------  -----  
 0   Country                          2938 non-null   object 
 1   Year                             2938 non-null   int64  
 2   Status                           2938 non-null   object 
 3   Life expectancy                  2928 non-null   float64
 4   Adult Mortality                  2928 non-null   float64
 5   infant deaths                    2938 non-null   int64  
 6   Alcohol                          2744 non-null   float64
 7   percentage expenditure           2938 non-null   float64
 8   Hepatitis B                      2385 non-null   float64
 9   Measles                          2938 non-null   int64  
 10   BMI                             2904 non-null   float64
 11  under-five deaths                2938 non-null   int64  
 12  Polio                            2919 non-null   float64
 13  Total expenditure                2712 non-null   float64
 14  Diphtheria                       2919 non-null   float64
 15   HIV/AIDS                        2938 non-null   float64
 16  GDP                              2490 non-null   float64
 17  Population                       2286 non-null   float64
 18   thinness  1-19 years            2904 non-null   float64
 19   thinness 5-9 years              2904 non-null   float64
 20  Income composition of resources  2771 non-null   float64
 21  Schooling                        2775 non-null   float64
dtypes: float64(16), int64(4), object(2)
memory usage: 505.1+ KB

df.columns

Index(['Country', 'Year', 'Status', 'Life expectancy ', 'Adult Mortality',
       'infant deaths', 'Alcohol', 'percentage expenditure', 'Hepatitis B',
       'Measles ', ' BMI ', 'under-five deaths ', 'Polio', 'Total expenditure',
       'Diphtheria ', ' HIV/AIDS', 'GDP', 'Population',
       ' thinness  1-19 years', ' thinness 5-9 years',
       'Income composition of resources', 'Schooling'],
      dtype='object')

# Borrando las columnas que no se van a utilizar en el análisis
df.drop(columns=['Status','Year','Country','percentage expenditure', 'under-five deaths ', ' HIV/AIDS', ' thinness 5-9 years'], axis=1, inplace=True)
df

df.describe()

df.shape

(2938, 15)

# Revisando los valores nulos
df.isnull().sum()

Life expectancy                     10
Adult Mortality                     10
infant deaths                        0
Alcohol                            194
Hepatitis B                        553
Measles                              0
 BMI                                34
Polio                               19
Total expenditure                  226
Diphtheria                          19
GDP                                448
Population                         652
 thinness  1-19 years               34
Income composition of resources    167
Schooling                          163
dtype: int64

# Analizando los valores faltantes 
df[df.isnull().any(axis=1)]

# Identificando qué tipo de valores faltantes existen, si son MCAR, MAR o MNAR
# Prueba de correlaciones en aquellos valores vacíos

# Guardando los registro con valores faltantes
missing_values = df[df.isnull().any(axis=1)]
missing_values

# Revisando la correlación de los valores faltantes
missing_values.corr()

import seaborn as sns
import matplotlib.pyplot as plt

plt.figure(figsize=(10, 6))
sns.heatmap(missing_values.corr(), annot=True)
plt.show()

# Graficando cada variable vs la columna "Life expectancy "
import matplotlib.pyplot as plt
import seaborn as sns

# Gráficas acomodadas en 4x4 sin la gráfica Light expectancy vs Light expectancy
fig, axs = plt.subplots(4, 4, figsize=(20, 20))
for i, column in enumerate(df.columns):
    if column != 'Life expectancy ':
        sns.scatterplot(data=df, x=column, y='Life expectancy ', ax=axs[i // 4, i % 4])

import numpy as np
import numpy.linalg as ln

# Implementando la fórmula directa de Regresión lineal múltiple
df_clean = df.dropna()
X = df_clean.drop(columns='Life expectancy ')
y = df_clean['Life expectancy ']

X_np = X.to_numpy()
y_np = y.to_numpy()

X_np.shape, y_np.shape

((1649, 14), (1649,))

# Revisar si las matrices tienen valores vacios
np.isnan(X_np).sum(), np.isnan(y_np).sum()

(np.int64(0), np.int64(0))

print(X_np)

[[2.63e+02 6.20e+01 1.00e-02 ... 1.72e+01 4.79e-01 1.01e+01]
 [2.71e+02 6.40e+01 1.00e-02 ... 1.75e+01 4.76e-01 1.00e+01]
 [2.68e+02 6.60e+01 1.00e-02 ... 1.77e+01 4.70e-01 9.90e+00]
 ...
 [7.30e+01 2.50e+01 4.43e+00 ... 1.20e+00 4.27e-01 1.00e+01]
 [6.86e+02 2.50e+01 1.72e+00 ... 1.60e+00 4.27e-01 9.80e+00]
 [6.65e+02 2.40e+01 1.68e+00 ... 1.10e+01 4.34e-01 9.80e+00]]

# Eror de Gradiente 
def grad(X, y, beta):
    n = len(y)
    y_pred = X @ beta
    res = y - y_pred
    tmp = res[:,np.newaxis] * X # Esto sirve para operar elemento a elemento
    return -2/n * tmp.sum(axis=0)

# Generando funcion de regresion lineal multiple
from sklearn.preprocessing import StandardScaler
def fit_model(X,y, alpha = .005,maxit = 10000):
    
    # Normalización de los datos
    scaler_X = StandardScaler()
    X_scaled = scaler_X.fit_transform(X)

    scaler_y = StandardScaler()
    y_scaled = scaler_y.fit_transform(y.reshape(-1, 1)).flatten()

    # de predictores
    n = X.shape[1]
    #print(f"Numero de predictores: {n}")

    #Inicializando beta
    beta = 2*np.random.rand(n) - 1.0
    #print(f"Beta inicial: {beta}")

    #Optimizando el algoritmo
    it = 0
    while (np.linalg.norm(grad(X_scaled, y_scaled, beta)) > 1e-4) and (it < maxit):
        beta = beta - alpha * grad(X_scaled, y_scaled, beta)
        
        # Chequeo para valores extremos de beta
        if np.any(np.abs(beta) > 1e10):  # Si algún valor en beta es extremadamente grande
            print(f"Warning: Valores de Beta empieza a hacerse grandes en iteración {it}")
            break

        # Chequeo de NaN en beta
        if np.any(np.isnan(beta)):
            print(f"NaN se detectó en la iteración {it}")
            break

        it = it + 1
        #print(it)
    return beta, scaler_X, scaler_y

# Modelo de regresion lineal multiple

beta = fit_model(X_np, y_np)
print("Los coeficientes son: ", beta)

Los coeficientes son:  (array([-0.41557125, -0.02833773, -0.07918307, -0.00251173,  0.00986548,
        0.08712028,  0.02295472, -0.00678517,  0.05081052,  0.08809878,
        0.0220853 , -0.04523112,  0.23104851,  0.28071011]), StandardScaler(), StandardScaler())

from sklearn.model_selection import KFold
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from sklearn.model_selection import train_test_split
from sklearn.model_selection import LeavePOut
from sklearn.model_selection import LeaveOneOut

import warnings
from sklearn.exceptions import UndefinedMetricWarning

# Suprimir los warnings de tipo UndefinedMetricWarning
warnings.simplefilter(action='ignore', category=UndefinedMetricWarning)

# Funcion para predecir
def predict(X, beta, scaler_X, scaler_y):
    X_scaled = scaler_X.transform(X)  # Normalizar las nuevas entradas
    y_pred_scaled = X_scaled @ beta
    y_pred = scaler_y.inverse_transform(y_pred_scaled.reshape(-1, 1)).flatten()  # Desnormalizar
    return y_pred

# Evaluando con validación cruzada
def validacion_cruzada(X, y, k):
    kf = KFold(n_splits=k, shuffle=True)

    mse_cv = []
    mae_cv = []
    r2_cv = []
    for train_index, test_index in kf.split(X):

        # Fase de entrenamiento
        X_train, y_train = X[train_index, :], y[train_index]
        beta_cv, scaler_X, scaler_y = fit_model(X_train, y_train)

        # Fase de prueba
        X_test, y_test = X[test_index, :], y[test_index]
        y_pred = predict(X_test, beta_cv, scaler_X, scaler_y)

        # Calcular MSE, MAE y R^2
        mse_i = mean_squared_error(y_test, y_pred)
        print('MSE = ', mse_i)
        mse_cv.append(mse_i)

        mae_i = mean_absolute_error(y_test, y_pred)
        print('MAE = ', mae_i)
        mae_cv.append(mae_i)

        r2_i = r2_score(y_test, y_pred)
        print('R^2 = ', r2_i)
        r2_cv.append(r2_i)

    print('MSE Promedio:', np.average(mse_cv), '  MAE Promedio:', np.average(mae_cv), '  R^2 Promedio:', np.average(r2_cv))

# Revisando si X_np y y_np tienen valores nulos
#np.isnan(X_np).sum(), np.isnan(y_np).sum()

validacion_cruzada(X_np, y_np, 5)

MSE =  20.361671522748033
MAE =  3.246274965738945
R^2 =  0.7528717589438239
MSE =  22.221650655769384
MAE =  3.2581433266346025
R^2 =  0.7270027093880594
MSE =  15.58103223835667
MAE =  3.003647878204671
R^2 =  0.7221703681355872
MSE =  17.27218951181445
MAE =  2.979266206194986
R^2 =  0.7693544342873956
MSE =  18.51895080880482
MAE =  3.1379932391455836
R^2 =  0.7949390405075046
MSE Promedio: 18.79109894749867   MAE Promedio: 3.125065123183757   R^2 Promedio: 0.7532676622524741

def monte_carlo_cross_validation(X, y, n_iterations, test_size=0.2):

    mse_cv = []
    mae_cv = []
    r2_cv = []

    for _ in range(n_iterations):
        # Dividir los datos en conjunto de entrenamiento y conjunto de prueba
        X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=test_size)
        
        # Ajustar el modelo en el conjunto de entrenamiento
        beta, scaler_X, scaler_y = fit_model(X_train, y_train)
        
        # Hacer predicciones en el conjunto de prueba
        y_pred = predict(X_test, beta, scaler_X, scaler_y)
        
         # Calcular MSE, MAE y R^2
        mse_i = mean_squared_error(y_test, y_pred)
        #print('MSE = ', mse_i)
        mse_cv.append(mse_i)

        mae_i = mean_absolute_error(y_test, y_pred)
        #print('MAE = ', mae_i)
        mae_cv.append(mae_i)

        r2_i = r2_score(y_test, y_pred)
        #print('R^2 = ', r2_i)
        r2_cv.append(r2_i)

        # Porcentaje de completado del proceso pero eliminando la impresión de cada iteración
        print(f'Iteración {_ + 1}/{n_iterations}', end='\r')

    print('MSE Promedio:', np.average(mse_cv), '  MAE Promedio:', np.average(mae_cv), '  R^2 Promedio:', np.average(r2_cv))
    return np.average(mse_cv), np.average(mae_cv), np.average(r2_cv), mse_cv, mae_cv, r2_cv

# Evaluando con método Monte Carlo
msve_avg, mae_avg, r2_avg, msve, mae, r2 = monte_carlo_cross_validation(X_np, y_np, n_iterations=1000)
print(msve_avg, mae_avg, r2_avg)

MSE Promedio: 18.734391304381823   MAE Promedio: 3.118279494404135   R^2 Promedio: 0.7564712964804281
18.734391304381823 3.118279494404135 0.7564712964804281

MC_mse = msve
MC_mae = mae
MC_r2 = r2

MC_mse_avg = msve_avg
MC_mae_avg = mae_avg
MC_r2_avg = r2_avg


print(f'MSE: {MC_mse_avg}, MAE: {MC_mae_avg}, R^2: {MC_r2_avg}')

MSE: 18.734391304381823, MAE: 3.118279494404135, R^2: 0.7564712964804281

# Generando histograma de MSE y MAE
plt.figure(figsize=(20, 5))
plt.subplot(1, 3, 1)
plt.hist(MC_mse, bins=30, color='blue', edgecolor='black', rwidth=0.70, density=True)
plt.title('Histograma MSE para Monte Carlo')
plt.xlabel('MSE')
plt.ylabel('Frecuencia')

plt.subplot(1, 3, 2)
plt.hist(MC_mae, bins=30, color='green', edgecolor='black', rwidth=0.70, density=True)
plt.title('Histograma MAE para Monte Carlo')
plt.xlabel('MAE')
plt.ylabel('Frecuencia')

plt.show()

def leave_p_out_cross_validation(X, y, p):

    # Calculando las particiones necesarias
    lpo = LeavePOut(p)

    mse_cv = []
    mae_cv = []
    r2_cv = []
    
    i = 0
    it = lpo.get_n_splits(X)
    print(f'Número de particiones: {it}')
    for train_index, test_index in lpo.split(X):

        # Fase de entrenamiento
        X_train, y_train = X[train_index, :], y[train_index]
        beta_cv, scaler_X, scaler_y = fit_model(X_train, y_train)

        # Fase de prueba
        X_test, y_test = X[test_index, :], y[test_index]
        y_pred = predict(X_test, beta_cv, scaler_X, scaler_y)

        # Calcular MSE, MAE y R^2
        mse_i = mean_squared_error(y_test, y_pred)
        #print('MSE = ', mse_i)
        mse_cv.append(mse_i)

        mae_i = mean_absolute_error(y_test, y_pred)
        #print('MAE = ', mae_i)
        mae_cv.append(mae_i)

        r2_i = r2_score(y_test, y_pred)
        #print('R^2 = ', r2_i)
        r2_cv.append(r2_i)

        i += 1
        # Calculando el procentaje de avance
        percent = i * 100 / it
        print(f'Porcentaje de avance: ({percent}%)', end='\r')



    print('MSE Promedio:', np.average(mse_cv), '  MAE Promedio:', np.average(mae_cv), '  R^2 Promedio:', np.average(r2_cv))

leave_p_out_cross_validation(X_np, y_np, p=2)

Número de particiones: 1358776
(4.950116869888782%))))))

---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Cell In[1686], line 1
----> 1 leave_p_out_cross_validation(X_np, y_np, p=2)

Cell In[1685], line 17, in leave_p_out_cross_validation(X, y, p)
     13 for train_index, test_index in lpo.split(X):
     14 
     15     # Fase de entrenamiento
     16     X_train, y_train = X[train_index, :], y[train_index]
---> 17     beta_cv, scaler_X, scaler_y = fit_model(X_train, y_train)
     19     # Fase de prueba
     20     X_test, y_test = X[test_index, :], y[test_index]

Cell In[1665], line 23, in fit_model(X, y, alpha, maxit)
     21 it = 0
     22 while (np.linalg.norm(grad(X_scaled, y_scaled, beta)) > 1e-4) and (it < maxit):
---> 23     beta = beta - alpha * grad(X_scaled, y_scaled, beta)
     25     # Chequeo para valores extremos de beta
     26     if np.any(np.abs(beta) > 1e10):  # Si algún valor en beta es extremadamente grande

Cell In[1664], line 7, in grad(X, y, beta)
      5 res = y - y_pred
      6 tmp = res[:,np.newaxis] * X # Esto sirve para operar elemento a elemento
----> 7 return -2/n * tmp.sum(axis=0)

File c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\numpy\_core\_methods.py:52, in _sum(a, axis, dtype, out, keepdims, initial, where)
     50 def _sum(a, axis=None, dtype=None, out=None, keepdims=False,
     51          initial=_NoValue, where=True):
---> 52     return umr_sum(a, axis, dtype, out, keepdims, initial, where)

KeyboardInterrupt:

# Generando método de validación cruzada con LOOCV debido al tiempo de tardía de LPoCV

def leave_one_out_cross_validation(X, y):
    # Calculando las particiones necesarias
    loo = LeaveOneOut()

    mse_cv = []
    mae_cv = []
    r2_cv = []
    
    i = 0
    it = loo.get_n_splits(X)
    print(f'Número de particiones: {it}')
    for train_index, test_index in loo.split(X):

        # Fase de entrenamiento
        X_train, y_train = X[train_index, :], y[train_index]
        beta_cv, scaler_X, scaler_y = fit_model(X_train, y_train)

        # Fase de prueba
        X_test, y_test = X[test_index, :], y[test_index]
        y_pred = predict(X_test, beta_cv, scaler_X, scaler_y)

        # Calcular MSE, MAE y R^2
        mse_i = mean_squared_error(y_test, y_pred)
        #print('MSE = ', mse_i)
        mse_cv.append(mse_i)

        mae_i = mean_absolute_error(y_test, y_pred)
        #print('MAE = ', mae_i)
        mae_cv.append(mae_i)

        r2_i = r2_score(y_test, y_pred)
        #print('R^2 = ', r2_i)
        r2_cv.append(r2_i)

        i += 1
        # Calculando el procentaje de avance
        percent = round (i * 100 / it, 2)
        print(f'Porcentaje de avance: ({percent}%)', end='\r')



    print('MSE Promedio:', np.average(mse_cv), '  MAE Promedio:', np.average(mae_cv), '  R^2 Promedio:', np.average(r2_cv))
    return np.average(mse_cv), np.average(mae_cv), np.average(r2_cv), mse_cv, mae_cv, r2_cv

LOOCV_msve_avg, LOOCV_mae_avg, LOOCV_r2_avg, LOOCV_msve, LOOCV_mae, LOOCV_r2 = leave_one_out_cross_validation(X_np, y_np)

Número de particiones: 1649
MSE Promedio: 18.61551424388183   MAE Promedio: 3.110112329306491   R^2 Promedio: nan

# Generando histograma de MSE y MAE
plt.figure(figsize=(20, 5))
plt.subplot(1, 3, 1)
plt.hist(LOOCV_msve, bins=30, color='blue', edgecolor='black', rwidth=0.70, density=True)
plt.title('Histograma MSE para LOOCV')
plt.xlabel('MSE')
plt.ylabel('Frecuencia')
plt.xlim(0, 200)

# Reduciendo escalas para visualizar mejor el histograma

plt.subplot(1, 3, 2)
plt.hist(LOOCV_mae, bins=30, color='green', edgecolor='black', rwidth=0.70, density=True)
plt.title('Histograma MAE para LOOCV')
plt.xlabel('MAE')
plt.ylabel('Frecuencia')

plt.show()

df_clean

df_clean_2 = df_clean.copy()
df_clean_2

# Agregando el cuadrado de cada variable excepto "Life expectancy"
for column in df_clean_2.columns:
    if column != 'Life expectancy ':
        df_clean_2[f'{column}^2'] = df_clean_2[column] ** 2
df_clean_2

# Agregando el producto de cada par de variables excepto "Life expectancy", X1*X2 X3*X4, etc.
life_expectancy = df_clean_2["Life expectancy "]

# Filtrar las columnas que no sean cuadradas
non_squared_columns = [col for col in df_clean_2.columns if not col.endswith('^2')]
df_filtered = df_clean_2[non_squared_columns]
df_filtered.drop(columns='Life expectancy ', inplace=True)
#print(df_filtered)

products_df = pd.DataFrame()

for i in range(0, len(df_filtered.columns) - 1, 2):
    col1 = df_filtered.columns[i]
    col2 = df_filtered.columns[i + 1]
    
    products_df[f'{col1}*{col2}'] = df_filtered[col1] * df_filtered[col2]

# Recuperar las columnas cuadradas para agregarlas después
squared_columns = [col for col in df_clean_2.columns if col.endswith('^2')]
squared_df = df_clean_2[squared_columns]

final_df = pd.concat([df_clean_2, squared_df, products_df], axis=1)

final_df

C:\Users\palmi\AppData\Local\Temp\ipykernel_50008\643249155.py:7: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  df_filtered.drop(columns='Life expectancy ', inplace=True)

final_df.info()

<class 'pandas.core.frame.DataFrame'>
Index: 1649 entries, 0 to 2937
Data columns (total 50 columns):
 #   Column                                     Non-Null Count  Dtype  
---  ------                                     --------------  -----  
 0   Life expectancy                            1649 non-null   float64
 1   Adult Mortality                            1649 non-null   float64
 2   infant deaths                              1649 non-null   int64  
 3   Alcohol                                    1649 non-null   float64
 4   Hepatitis B                                1649 non-null   float64
 5   Measles                                    1649 non-null   int64  
 6    BMI                                       1649 non-null   float64
 7   Polio                                      1649 non-null   float64
 8   Total expenditure                          1649 non-null   float64
 9   Diphtheria                                 1649 non-null   float64
 10  GDP                                        1649 non-null   float64
 11  Population                                 1649 non-null   float64
 12   thinness  1-19 years                      1649 non-null   float64
 13  Income composition of resources            1649 non-null   float64
 14  Schooling                                  1649 non-null   float64
 15  Adult Mortality^2                          1649 non-null   float64
 16  infant deaths^2                            1649 non-null   int64  
 17  Alcohol^2                                  1649 non-null   float64
 18  Hepatitis B^2                              1649 non-null   float64
 19  Measles ^2                                 1649 non-null   int64  
 20   BMI ^2                                    1649 non-null   float64
 21  Polio^2                                    1649 non-null   float64
 22  Total expenditure^2                        1649 non-null   float64
 23  Diphtheria ^2                              1649 non-null   float64
 24  GDP^2                                      1649 non-null   float64
 25  Population^2                               1649 non-null   float64
 26   thinness  1-19 years^2                    1649 non-null   float64
 27  Income composition of resources^2          1649 non-null   float64
 28  Schooling^2                                1649 non-null   float64
 29  Adult Mortality^2                          1649 non-null   float64
 30  infant deaths^2                            1649 non-null   int64  
 31  Alcohol^2                                  1649 non-null   float64
 32  Hepatitis B^2                              1649 non-null   float64
 33  Measles ^2                                 1649 non-null   int64  
 34   BMI ^2                                    1649 non-null   float64
 35  Polio^2                                    1649 non-null   float64
 36  Total expenditure^2                        1649 non-null   float64
 37  Diphtheria ^2                              1649 non-null   float64
 38  GDP^2                                      1649 non-null   float64
 39  Population^2                               1649 non-null   float64
 40   thinness  1-19 years^2                    1649 non-null   float64
 41  Income composition of resources^2          1649 non-null   float64
 42  Schooling^2                                1649 non-null   float64
 43  Adult Mortality*infant deaths              1649 non-null   float64
 44  Alcohol*Hepatitis B                        1649 non-null   float64
 45  Measles * BMI                              1649 non-null   float64
 46  Polio*Total expenditure                    1649 non-null   float64
 47  Diphtheria *GDP                            1649 non-null   float64
 48  Population* thinness  1-19 years           1649 non-null   float64
 49  Income composition of resources*Schooling  1649 non-null   float64
dtypes: float64(44), int64(6)
memory usage: 657.0 KB

#print(final_df.columns[29])
#print(final_df.columns[0])
final_df.iloc[:, 15:43].head(5)
#final_df.head(5)

print(final_df.columns)
print(final_df.shape)

Index(['Life expectancy ', 'Adult Mortality', 'infant deaths', 'Alcohol',
       'Hepatitis B', 'Measles ', ' BMI ', 'Polio', 'Total expenditure',
       'Diphtheria ', 'GDP', 'Population', ' thinness  1-19 years',
       'Income composition of resources', 'Schooling', 'Adult Mortality^2',
       'infant deaths^2', 'Alcohol^2', 'Hepatitis B^2', 'Measles ^2',
       ' BMI ^2', 'Polio^2', 'Total expenditure^2', 'Diphtheria ^2', 'GDP^2',
       'Population^2', ' thinness  1-19 years^2',
       'Income composition of resources^2', 'Schooling^2', 'Adult Mortality^2',
       'infant deaths^2', 'Alcohol^2', 'Hepatitis B^2', 'Measles ^2',
       ' BMI ^2', 'Polio^2', 'Total expenditure^2', 'Diphtheria ^2', 'GDP^2',
       'Population^2', ' thinness  1-19 years^2',
       'Income composition of resources^2', 'Schooling^2',
       'Adult Mortality*infant deaths', 'Alcohol*Hepatitis B',
       'Measles * BMI ', 'Polio*Total expenditure', 'Diphtheria *GDP',
       'Population* thinness  1-19 years',
       'Income composition of resources*Schooling'],
      dtype='object')
(1649, 50)

final_df = final_df.loc[:,~final_df.columns.duplicated()]
print(final_df.columns)
final_df

Index(['Life expectancy ', 'Adult Mortality', 'infant deaths', 'Alcohol',
       'Hepatitis B', 'Measles ', ' BMI ', 'Polio', 'Total expenditure',
       'Diphtheria ', 'GDP', 'Population', ' thinness  1-19 years',
       'Income composition of resources', 'Schooling', 'Adult Mortality^2',
       'infant deaths^2', 'Alcohol^2', 'Hepatitis B^2', 'Measles ^2',
       ' BMI ^2', 'Polio^2', 'Total expenditure^2', 'Diphtheria ^2', 'GDP^2',
       'Population^2', ' thinness  1-19 years^2',
       'Income composition of resources^2', 'Schooling^2',
       'Adult Mortality*infant deaths', 'Alcohol*Hepatitis B',
       'Measles * BMI ', 'Polio*Total expenditure', 'Diphtheria *GDP',
       'Population* thinness  1-19 years',
       'Income composition of resources*Schooling'],
      dtype='object')

# Graficando X vs y evitando la gráfica de Life expectancy vs Life expectancy
import matplotlib.pyplot as plt
import seaborn as sns
# Número de gráficos que necesitas
columns_to_plot = [col for col in final_df.columns if col != 'Life expectancy ']
num_graphs = len(columns_to_plot)

ncols = 2  # Número de columnas fijas
nrows = int(np.ceil(num_graphs / ncols))  # Calcula el número de filas necesarias


fig, axs = plt.subplots(nrows, ncols, figsize=(20, nrows * 5))
axs = axs.flatten()

for i, column in enumerate(columns_to_plot):
    sns.scatterplot(data=final_df, x=column, y='Life expectancy ', ax=axs[i])

# Desactivar los subplots no utilizados
for j in range(num_graphs, len(axs)):
    fig.delaxes(axs[j])

plt.tight_layout()
plt.show()

# Implementando la fórmula directa de Regresión lineal múltiple
X = final_df.drop(columns='Life expectancy ')
y = final_df['Life expectancy ']

X_np = X.to_numpy()
y_np = y.to_numpy()

X_np.shape, y_np.shape

((1649, 35), (1649,))

# Modelo de regresion lineal multiple
beta = fit_model(X_np, y_np)
print("Los coeficientes son: ", beta)

Los coeficientes son:  (array([ 0.07276329, -0.10340446, -0.18210298,  0.20016337,  0.01268828,
        0.01539157, -0.08500526,  0.03393918, -0.36242215,  0.73686881,
        0.00988002, -0.37648582, -0.10607508,  0.19752976, -0.42329008,
       -0.03182842, -0.05542406, -0.29576641,  0.01969459,  0.01880983,
        0.05652631, -0.04241047,  0.53265629, -0.00836126, -0.05081046,
        0.39384124,  1.02055566,  0.11094838,  0.02090734,  0.11747444,
        0.0092962 ,  0.03622271, -0.70230681,  0.05100309, -0.64385561]), StandardScaler(), StandardScaler())

validacion_cruzada(X_np, y_np, 5)

MSE =  14.274511460132596
MAE =  2.553970031570719
R^2 =  0.8008212715563825
MSE =  10.82209179044934
MAE =  2.519580199297883
R^2 =  0.853794312214851
MSE =  10.014386510878426
MAE =  2.331230425474868
R^2 =  0.8696006441716084
MSE =  11.45547159411425
MAE =  2.476862924703758
R^2 =  0.8639939852960448
MSE =  11.77069167530588
MAE =  2.407790285488747
R^2 =  0.8517197079066726
MSE Promedio: 11.667430606176097   MAE Promedio: 2.457886773307195   R^2 Promedio: 0.847985984229112

# Generando regersión Ridge con descenso de gradientes para df_clean

def grad_ridge(X, y, beta, alpha, lamb):
    n = len(y)
    y_pred = X @ beta
    res = y - y_pred
    tmp = res[:,np.newaxis] * X # Esto sirve para operar elemento a elemento
    return -2/n * tmp.sum(axis=0) + 2*lamb*beta

# Generando regersión Ridge con descenso de gradientes para df_clean

def fit_model_ridge(X,y, alpha, maxit, lamb):
        
        # Normalización de los datos
        scaler_X = StandardScaler()
        X_scaled = scaler_X.fit_transform(X)
    
        scaler_y = StandardScaler()
        y_scaled = scaler_y.fit_transform(y.reshape(-1, 1)).flatten()
    
        # de predictores
        n = X.shape[1]
        #print(f"Numero de predictores: {n}")
    
        #Inicializando beta
        beta = 2*np.random.rand(n) - 1.0
        #print(f"Beta inicial: {beta}")
    
        #Optimizando el algoritmo
        it = 0
        while (np.linalg.norm(grad_ridge(X_scaled, y_scaled, beta, alpha, lamb)) > 1e-4) and (it < maxit):
            beta = beta - alpha * grad_ridge(X_scaled, y_scaled, beta, alpha, lamb)
            
            # Chequeo para valores extremos de beta
            if np.any(np.abs(beta) > 1e10):  # Si algún valor en beta es extremadamente grande
                afafa = 0
                #print(f"Warning: Valores de Beta empieza a hacerse grandes en iteración {it}")
                #break
    
            # Chequeo de NaN en beta
            if np.any(np.isnan(beta)):
                print(f"NaN se detectó en la iteración {it}")
                break
    
            it = it + 1
            #print(it)
        return beta, scaler_X, scaler_y

df_clean_ridge = df_clean.copy()
X = df_clean_ridge.drop(columns='Life expectancy ')
y = df_clean_ridge['Life expectancy ']

X_np = X.to_numpy()
y_np = y.to_numpy()

X_np.shape, y_np.shape

((1649, 14), (1649,))

beta = fit_model_ridge(X_np, y_np, alpha=0.005, maxit=10000, lamb=0.1)
print("Los coeficientes son: ", beta)

Los coeficientes son:  (array([-0.38303956, -0.02280727, -0.05172093,  0.0017243 ,  0.00770393,
        0.09641199,  0.02974441, -0.00401481,  0.0504755 ,  0.08888828,
        0.02065827, -0.05218345,  0.22319087,  0.2470206 ]), StandardScaler(), StandardScaler())

# Definimos los valores de lambda en una escala logarítmica
alphas = np.logspace(-2, 2, 100)
coefs = []
#print(alphas)

scaler = StandardScaler()
X_scaled = scaler.fit_transform(X_np)

# Bucle para ajustar el modelo a cada valor de lambda
for lamb in alphas:
    beta, _, _ = fit_model_ridge(X_np, y_np, alpha=.005, maxit=1000, lamb=lamb)
    coefs.append(beta)


coefs = np.array(coefs)

# Generamos la gráfica
fig, ax = plt.subplots(figsize=(10, 6))
ax.plot(alphas, coefs)

ax.set_xscale('log')
#Nota de que variable pertenece a qué color acomodada a la izquierda del plot
ax.legend(X.columns, loc='center left', bbox_to_anchor=(1, 0.5))
ax.set_xlabel('lambda (Regularización)')
ax.set_ylabel('Coeficientes')
ax.set_title('Coeficientes del modelo en función de la regularización (lambda)')

plt.axis('tight')
plt.show()

from sklearn.linear_model import Ridge
alphas = np.logspace(-3, 6, 100)
coefs_sklearn = []
for lamb in alphas:
    ridge = Ridge(alpha=lamb, fit_intercept=False)
    ridge.fit(X_np, y_np)
    coefs_sklearn.append(ridge.coef_)

coefs_sklearn = np.array(coefs_sklearn)

# Generamos la gráfica
fig, ax = plt.subplots(figsize=(10, 6))
ax.plot(alphas, coefs_sklearn)

ax.set_xscale('log')
ax.legend(X.columns, loc='center left', bbox_to_anchor=(1, 0.5))
ax.set_xlabel('lambda (Regularización)')
ax.set_ylabel('Coeficientes')
ax.set_title('Coeficientes del modelo en función de la regularización (lambda)')
plt.axis('tight')
plt.show()

c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.14305e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.14308e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.14311e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.14315e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.1432e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.14326e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.14333e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.14342e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.14354e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.14367e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.14385e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.14406e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.14432e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.14464e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.14504e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.14552e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.14613e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.14687e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.14778e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.14891e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.1503e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.15202e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.15413e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.15673e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.15995e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.16391e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.16879e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.17481e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.18223e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.19138e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.20266e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.21657e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.23371e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.25485e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.28091e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.31303e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.35264e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.40147e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.46167e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.53588e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.62738e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.74019e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.87926e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=3.05071e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=3.2621e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=3.52271e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=3.844e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=4.24013e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=4.72851e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=5.33063e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=6.073e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=6.9883e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=8.11681e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=9.50825e-18): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=1.12239e-17): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=1.33394e-17): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=1.5948e-17): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=1.91647e-17): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.31316e-17): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=2.80211e-17): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=3.40503e-17): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=4.14853e-17): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=5.06545e-17): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=6.19629e-17): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=7.59109e-17): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_ridge.py:216: LinAlgWarning: Ill-conditioned matrix (rcond=9.31162e-17): result may not be accurate.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T

from sklearn.linear_model import Lasso

coefs_lasso = []
for lamb in alphas:
    lasso = Lasso(alpha=lamb, fit_intercept=False)
    lasso.fit(X_np, y_np)
    coefs_lasso.append(lasso.coef_)

coefs_lasso = np.array(coefs_lasso)

# Generamos la gráfica
fig, ax = plt.subplots(figsize=(10, 6))
ax.plot(alphas, coefs_lasso)

ax.set_xscale('log')
ax.legend(X.columns, loc='center left', bbox_to_anchor=(1, 0.5))
ax.set_xlabel('lambda (Regularización)')
ax.set_ylabel('Coeficientes')
ax.set_title('Coeficientes del modelo en función de la regularización (lambda)')
plt.axis('tight')
plt.show()

c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_coordinate_descent.py:697: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 2.521e+04, tolerance: 8.047e+02
  model = cd_fast.enet_coordinate_descent(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\linear_model\_coordinate_descent.py:697: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 2.208e+04, tolerance: 8.047e+02
  model = cd_fast.enet_coordinate_descent(

from ucimlrepo import fetch_ucirepo 
  
# fetch dataset 
parkinsons_telemonitoring = fetch_ucirepo(id=189) 
  
# data (as pandas dataframes) 
X = parkinsons_telemonitoring.data.features 
y = parkinsons_telemonitoring.data.targets 
  
print(X)
print(y)
print(X.shape)
print(y.shape)

# metadata 
print(parkinsons_telemonitoring.metadata) 
  
# variable information 
print(parkinsons_telemonitoring.variables)

      age  test_time  Jitter(%)  Jitter(Abs)  Jitter:RAP  Jitter:PPQ5  \
0      72     5.6431    0.00662     0.000034     0.00401      0.00317   
1      72    12.6660    0.00300     0.000017     0.00132      0.00150   
2      72    19.6810    0.00481     0.000025     0.00205      0.00208   
3      72    25.6470    0.00528     0.000027     0.00191      0.00264   
4      72    33.6420    0.00335     0.000020     0.00093      0.00130   
...   ...        ...        ...          ...         ...          ...   
5870   61   142.7900    0.00406     0.000031     0.00167      0.00168   
5871   61   149.8400    0.00297     0.000025     0.00119      0.00147   
5872   61   156.8200    0.00349     0.000025     0.00152      0.00187   
5873   61   163.7300    0.00281     0.000020     0.00128      0.00151   
5874   61   170.7300    0.00282     0.000021     0.00135      0.00166   

      Jitter:DDP  Shimmer  Shimmer(dB)  Shimmer:APQ3  Shimmer:APQ5  \
0        0.01204  0.02565        0.230       0.01438       0.01309   
1        0.00395  0.02024        0.179       0.00994       0.01072   
2        0.00616  0.01675        0.181       0.00734       0.00844   
3        0.00573  0.02309        0.327       0.01106       0.01265   
4        0.00278  0.01703        0.176       0.00679       0.00929   
...          ...      ...          ...           ...           ...   
5870     0.00500  0.01896        0.160       0.00973       0.01133   
5871     0.00358  0.02315        0.215       0.01052       0.01277   
5872     0.00456  0.02499        0.244       0.01371       0.01456   
5873     0.00383  0.01484        0.131       0.00693       0.00870   
5874     0.00406  0.01907        0.171       0.00946       0.01154   

      Shimmer:APQ11  Shimmer:DDA       NHR     HNR     RPDE      DFA      PPE  \
0           0.01662      0.04314  0.014290  21.640  0.41888  0.54842  0.16006   
1           0.01689      0.02982  0.011112  27.183  0.43493  0.56477  0.10810   
2           0.01458      0.02202  0.020220  23.047  0.46222  0.54405  0.21014   
3           0.01963      0.03317  0.027837  24.445  0.48730  0.57794  0.33277   
4           0.01819      0.02036  0.011625  26.126  0.47188  0.56122  0.19361   
...             ...          ...       ...     ...      ...      ...      ...   
5870        0.01549      0.02920  0.025137  22.369  0.64215  0.55314  0.21367   
5871        0.01904      0.03157  0.011927  22.886  0.52598  0.56518  0.12621   
5872        0.01877      0.04112  0.017701  25.065  0.47792  0.57888  0.14157   
5873        0.01307      0.02078  0.007984  24.422  0.56865  0.56327  0.14204   
5874        0.01470      0.02839  0.008172  23.259  0.58608  0.57077  0.15336   

      sex  
0       0  
1       0  
2       0  
3       0  
4       0  
...   ...  
5870    0  
5871    0  
5872    0  
5873    0  
5874    0  

[5875 rows x 19 columns]
      motor_UPDRS  total_UPDRS
0          28.199       34.398
1          28.447       34.894
2          28.695       35.389
3          28.905       35.810
4          29.187       36.375
...           ...          ...
5870       22.485       33.485
5871       21.988       32.988
5872       21.495       32.495
5873       21.007       32.007
5874       20.513       31.513

[5875 rows x 2 columns]
(5875, 19)
(5875, 2)
{'uci_id': 189, 'name': 'Parkinsons Telemonitoring', 'repository_url': 'https://archive.ics.uci.edu/dataset/189/parkinsons+telemonitoring', 'data_url': 'https://archive.ics.uci.edu/static/public/189/data.csv', 'abstract': "Oxford Parkinson's Disease Telemonitoring Dataset", 'area': 'Health and Medicine', 'tasks': ['Regression'], 'characteristics': ['Tabular'], 'num_instances': 5875, 'num_features': 19, 'feature_types': ['Integer', 'Real'], 'demographics': ['Age', 'Sex'], 'target_col': ['motor_UPDRS', 'total_UPDRS'], 'index_col': ['subject#'], 'has_missing_values': 'no', 'missing_values_symbol': None, 'year_of_dataset_creation': 2009, 'last_updated': 'Fri Nov 03 2023', 'dataset_doi': '10.24432/C5ZS3N', 'creators': ['Athanasios Tsanas', 'Max Little'], 'intro_paper': {'title': "Accurate Telemonitoring of Parkinson's Disease Progression by Noninvasive Speech Tests", 'authors': 'A. Tsanas, Max A. Little, P. McSharry, L. Ramig', 'published_in': 'IEEE Transactions on Biomedical Engineering', 'year': 2010, 'url': 'https://www.semanticscholar.org/paper/1fdf33b6d8b1bdb38866ba824c1dcaecdfb6bdd6', 'doi': None}, 'additional_info': {'summary': "This dataset is composed of a range of biomedical voice measurements from 42 people with early-stage Parkinson's disease recruited to a six-month trial of a telemonitoring device for remote symptom progression monitoring. The recordings were automatically captured in the patient's homes.\r\n\r\nColumns in the table contain subject number, subject age, subject gender, time interval from baseline recruitment date, motor UPDRS, total UPDRS, and 16 biomedical voice measures. Each row corresponds to one of 5,875 voice recording from these individuals. The main aim of the data is to predict the motor and total UPDRS scores ('motor_UPDRS' and 'total_UPDRS') from the 16 voice measures.\r\n\r\nThe data is in ASCII CSV format. The rows of the CSV file contain an instance corresponding to one voice recording. There are around 200 recordings per patient, the subject number of the patient is identified in the first column. For further information or to pass on comments, please contact Athanasios Tsanas (tsanasthanasis@gmail.com) or Max Little (littlem@physics.ox.ac.uk).\r\n\r\nFurther details are contained in the following reference -- if you use this dataset, please cite:\r\nAthanasios Tsanas, Max A. Little, Patrick E. McSharry, Lorraine O. Ramig (2009),\r\n'Accurate telemonitoring of Parkinson’s disease progression by non-invasive speech tests',\r\nIEEE Transactions on Biomedical Engineering (to appear).\r\n\r\nFurther details about the biomedical voice measures can be found in:\r\nMax A. Little, Patrick E. McSharry, Eric J. Hunter, Lorraine O. Ramig (2009), \r\n'Suitability of dysphonia measurements for telemonitoring of Parkinson's disease', \r\nIEEE Transactions on Biomedical Engineering, 56(4):1015-1022\r\n", 'purpose': None, 'funded_by': None, 'instances_represent': None, 'recommended_data_splits': None, 'sensitive_data': None, 'preprocessing_description': None, 'variable_info': "subject# - Integer that uniquely identifies each subject\r\nage - Subject age\r\nsex - Subject gender '0' - male, '1' - female\r\ntest_time - Time since recruitment into the trial. The integer part is the number of days since recruitment. \r\nmotor_UPDRS - Clinician's motor UPDRS score, linearly interpolated\r\ntotal_UPDRS - Clinician's total UPDRS score, linearly interpolated\r\nJitter(%),Jitter(Abs),Jitter:RAP,Jitter:PPQ5,Jitter:DDP - Several measures of variation in fundamental frequency\r\nShimmer,Shimmer(dB),Shimmer:APQ3,Shimmer:APQ5,Shimmer:APQ11,Shimmer:DDA - Several measures of variation in amplitude\r\nNHR,HNR - Two measures of ratio of noise to tonal components in the voice\r\nRPDE - A nonlinear dynamical complexity measure\r\nDFA - Signal fractal scaling exponent\r\nPPE - A nonlinear measure of fundamental frequency variation \r\n", 'citation': None}}
             name     role        type demographic  \
0        subject#       ID     Integer        None   
1             age  Feature     Integer         Age   
2       test_time  Feature  Continuous        None   
3       Jitter(%)  Feature  Continuous        None   
4     Jitter(Abs)  Feature  Continuous        None   
5      Jitter:RAP  Feature  Continuous        None   
6     Jitter:PPQ5  Feature  Continuous        None   
7      Jitter:DDP  Feature  Continuous        None   
8         Shimmer  Feature  Continuous        None   
9     Shimmer(dB)  Feature  Continuous        None   
10   Shimmer:APQ3  Feature  Continuous        None   
11   Shimmer:APQ5  Feature  Continuous        None   
12  Shimmer:APQ11  Feature  Continuous        None   
13    Shimmer:DDA  Feature  Continuous        None   
14            NHR  Feature  Continuous        None   
15            HNR  Feature  Continuous        None   
16           RPDE  Feature  Continuous        None   
17            DFA  Feature  Continuous        None   
18            PPE  Feature  Continuous        None   
19    motor_UPDRS   Target  Continuous        None   
20    total_UPDRS   Target  Continuous        None   
21            sex  Feature      Binary         Sex   

                                          description units missing_values  
0       Integer that uniquely identifies each subject  None             no  
1                                         Subject age  None             no  
2   Time since recruitment into the trial. The int...  None             no  
3   Several measures of variation in fundamental f...  None             no  
4   Several measures of variation in fundamental f...  None             no  
5   Several measures of variation in fundamental f...  None             no  
6   Several measures of variation in fundamental f...  None             no  
7   Several measures of variation in fundamental f...  None             no  
8          Several measures of variation in amplitude  None             no  
9          Several measures of variation in amplitude  None             no  
10         Several measures of variation in amplitude  None             no  
11         Several measures of variation in amplitude  None             no  
12         Several measures of variation in amplitude  None             no  
13         Several measures of variation in amplitude  None             no  
14  Two measures of ratio of noise to tonal compon...  None             no  
15  Two measures of ratio of noise to tonal compon...  None             no  
16           A nonlinear dynamical complexity measure  None             no  
17                    Signal fractal scaling exponent  None             no  
18  A nonlinear measure of fundamental frequency v...  None             no  
19  Clinician's motor UPDRS score, linearly interp...  None             no  
20  Clinician's total UPDRS score, linearly interp...  None             no  
21               Subject sex '0' - male, '1' - female  None             no

y.drop(columns=['total_UPDRS'], axis=1, inplace=True)
y

C:\Users\palmi\AppData\Local\Temp\ipykernel_54828\1835047426.py:1: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  y.drop(columns=['total_UPDRS'], axis=1, inplace=True)

X.columns

Index(['age', 'test_time', 'Jitter(%)', 'Jitter(Abs)', 'Jitter:RAP',
       'Jitter:PPQ5', 'Jitter:DDP', 'Shimmer', 'Shimmer(dB)', 'Shimmer:APQ3',
       'Shimmer:APQ5', 'Shimmer:APQ11', 'Shimmer:DDA', 'NHR', 'HNR', 'RPDE',
       'DFA', 'PPE', 'sex'],
      dtype='object')

X.drop(columns=['test_time','Jitter:PPQ5','Shimmer:APQ3','NHR'], axis=1, inplace=True)
X

C:\Users\palmi\AppData\Local\Temp\ipykernel_54828\493501579.py:1: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  X.drop(columns=['test_time','Jitter:PPQ5','Shimmer:APQ3','NHR'], axis=1, inplace=True)

X.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 5875 entries, 0 to 5874
Data columns (total 15 columns):
 #   Column         Non-Null Count  Dtype  
---  ------         --------------  -----  
 0   age            5875 non-null   int64  
 1   Jitter(%)      5875 non-null   float64
 2   Jitter(Abs)    5875 non-null   float64
 3   Jitter:RAP     5875 non-null   float64
 4   Jitter:DDP     5875 non-null   float64
 5   Shimmer        5875 non-null   float64
 6   Shimmer(dB)    5875 non-null   float64
 7   Shimmer:APQ5   5875 non-null   float64
 8   Shimmer:APQ11  5875 non-null   float64
 9   Shimmer:DDA    5875 non-null   float64
 10  HNR            5875 non-null   float64
 11  RPDE           5875 non-null   float64
 12  DFA            5875 non-null   float64
 13  PPE            5875 non-null   float64
 14  sex            5875 non-null   int64  
dtypes: float64(13), int64(2)
memory usage: 688.6 KB

# Graficando cada variable vs la columna "motor_UPDRS"
import matplotlib.pyplot as plt
import seaborn as sns

# Transformando y a un array de una dimensión
y_arr = y.values.flatten()

fig, axs = plt.subplots(4, 4, figsize=(20, 20))

for i, column in enumerate(X.columns):
    if column != 'motor_UPDRS':
        sns.scatterplot(data=X, x=column, y=y_arr, ax=axs[i // 4, i % 4])
        axs[i // 4, i % 4].set_title(f'{column} vs motor_UPDRS')

# Ajustar el layout para que no se sobrepongan las gráficas
plt.tight_layout()
plt.show()

# Generando modelo de regresión lineal múltiple con librerías y haciendo validación cruzada
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import cross_val_score
import numpy as np

# Creando el modelo
model = LinearRegression()

# Realizando validación cruzada
scores = cross_val_score(model, X, y, cv=5, scoring='neg_mean_squared_error')

# Calculando el promedio de los scores
print(f"Error cuadrático medio: {round(np.mean(-scores),2)}")

Error cuadrático medio: 76.88%

df_X = X.copy()
df_y = y.copy()

df_X, df_y

(      age  Jitter(%)  Jitter(Abs)  Jitter:RAP  Jitter:DDP  Shimmer  \
 0      72    0.00662     0.000034     0.00401     0.01204  0.02565   
 1      72    0.00300     0.000017     0.00132     0.00395  0.02024   
 2      72    0.00481     0.000025     0.00205     0.00616  0.01675   
 3      72    0.00528     0.000027     0.00191     0.00573  0.02309   
 4      72    0.00335     0.000020     0.00093     0.00278  0.01703   
 ...   ...        ...          ...         ...         ...      ...   
 5870   61    0.00406     0.000031     0.00167     0.00500  0.01896   
 5871   61    0.00297     0.000025     0.00119     0.00358  0.02315   
 5872   61    0.00349     0.000025     0.00152     0.00456  0.02499   
 5873   61    0.00281     0.000020     0.00128     0.00383  0.01484   
 5874   61    0.00282     0.000021     0.00135     0.00406  0.01907   
 
       Shimmer(dB)  Shimmer:APQ5  Shimmer:APQ11  Shimmer:DDA     HNR     RPDE  \
 0           0.230       0.01309        0.01662      0.04314  21.640  0.41888   
 1           0.179       0.01072        0.01689      0.02982  27.183  0.43493   
 2           0.181       0.00844        0.01458      0.02202  23.047  0.46222   
 3           0.327       0.01265        0.01963      0.03317  24.445  0.48730   
 4           0.176       0.00929        0.01819      0.02036  26.126  0.47188   
 ...           ...           ...            ...          ...     ...      ...   
 5870        0.160       0.01133        0.01549      0.02920  22.369  0.64215   
 5871        0.215       0.01277        0.01904      0.03157  22.886  0.52598   
 5872        0.244       0.01456        0.01877      0.04112  25.065  0.47792   
 5873        0.131       0.00870        0.01307      0.02078  24.422  0.56865   
 5874        0.171       0.01154        0.01470      0.02839  23.259  0.58608   
 
           DFA      PPE  sex  
 0     0.54842  0.16006    0  
 1     0.56477  0.10810    0  
 2     0.54405  0.21014    0  
 3     0.57794  0.33277    0  
 4     0.56122  0.19361    0  
 ...       ...      ...  ...  
 5870  0.55314  0.21367    0  
 5871  0.56518  0.12621    0  
 5872  0.57888  0.14157    0  
 5873  0.56327  0.14204    0  
 5874  0.57077  0.15336    0  
 
 [5875 rows x 15 columns],
       motor_UPDRS
 0          28.199
 1          28.447
 2          28.695
 3          28.905
 4          29.187
 ...           ...
 5870       22.485
 5871       21.988
 5872       21.495
 5873       21.007
 5874       20.513
 
 [5875 rows x 1 columns])

import numpy as np
import pandas as pd
from sklearn.feature_selection import SelectKBest, f_regression
from sklearn.model_selection import cross_val_score, KFold
from sklearn.linear_model import LinearRegression
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import StandardScaler
from sklearn.feature_selection import SelectKBest, r_regression
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score

def filter__selection(x, y, n_features):
    print("----- Optimal selection of number of features -----")

    n_feats = n_features

    mse_nfeat = []
    mae_nfeat = []
    r2_nfeat = []
    for n_feat in n_feats:
        print('---- n features =', n_feat)
        
        mse_cv = []
        mae_cv = []
        r2_cv = []

        kf = KFold(n_splits=5, shuffle = True)

        for train_index, test_index in kf.split(x):
        
            # Training phase
            x_train = x[train_index, :]
            y_train = y[train_index]     
            
            fselection_cv = SelectKBest(r_regression, k = n_feat)
            fselection_cv.fit(x_train, y_train)
            x_train = fselection_cv.transform(x_train)

            regr_cv = LinearRegression()
            regr_cv.fit(x_train, y_train)

            # Test phase
            x_test = fselection_cv.transform(x[test_index, :])
            y_test = y[test_index]
            y_pred = regr_cv.predict(x_test)
        
            mse_i = mean_squared_error(y_test, y_pred)
            mse_cv.append(mse_i)
        
            mae_i = mean_absolute_error(y_test, y_pred)
            mae_cv.append(mae_i)

            r2_i = r2_score(y_test, y_pred)    
            r2_cv.append(r2_i)      
        

        mse = np.average(mse_cv)
        mse_nfeat.append(mse)
        
        mae = np.average(mae_cv)
        mae_nfeat.append(mae)
        
        r2 = np.average(r2_cv)
        r2_nfeat.append(r2)
        
        print('MSE:', mse, '  MAE:', mae,'  R^2:', r2)

    opt_index = np.argmin(mse_nfeat)
    opt_features = n_feats[opt_index]
    print("Optimal number of features: ", opt_features)

    fig, axs = plt.subplots(1, 3, tight_layout=True)
    axs[0].plot(n_feats, mse_nfeat)
    axs[0].set_xlabel("k")
    axs[0].set_ylabel("MSE")

    axs[1].plot(n_feats, mae_nfeat)
    axs[1].set_xlabel("k")
    axs[1].set_ylabel("MAE")

    axs[2].plot(n_feats, r2_nfeat)
    axs[2].set_xlabel("k")
    axs[2].set_ylabel("r^2")

    plt.show()

    return opt_features

X_np = df_X.to_numpy()
y_np = df_y.to_numpy().ravel()

#n_features = X_np.shape[1]
#n_features = np.arange(1, n_features + 1)
n_features = list(range(1, X_np.shape[1] + 1))
opt_features = filter__selection(X_np, y_np, n_features)

# Fit model with optimal number of features
regr = LinearRegression()
fselection = SelectKBest(r_regression, k = opt_features)
fselection.fit(X_np, y_np)

for i in range(len(fselection.get_support())): 
    if fselection.get_support()[i]:
        print("Selected features: ",df_X.columns[i])
print("Selected features: ", fselection.get_feature_names_out())

x_transformed = fselection.transform(X_np)
regr.fit(x_transformed, y)
print("Model coefficients: ", regr.coef_)
print("Model intercept: ", regr.intercept_)

----- Optimal selection of number of features -----
---- n features = 1
MSE: 61.18050430804374   MAE: 6.715571167507814   R^2: 0.0732131614795893
---- n features = 2
MSE: 60.04990390736022   MAE: 6.650276404388995   R^2: 0.09067836505141291
---- n features = 3
MSE: 60.03634675591476   MAE: 6.638499316453741   R^2: 0.09042654447251224
---- n features = 4
MSE: 60.03768081675141   MAE: 6.627608507088579   R^2: 0.09083604155507537
---- n features = 5
MSE: 59.78184462585343   MAE: 6.612851752854485   R^2: 0.0942793769460738
---- n features = 6
MSE: 59.692782998713824   MAE: 6.614683440751795   R^2: 0.0957268557724256
---- n features = 7
MSE: 59.595518253759636   MAE: 6.612527029012449   R^2: 0.0971021308047634
---- n features = 8
MSE: 59.58193378859703   MAE: 6.611305188832196   R^2: 0.09763615667853402
---- n features = 9
MSE: 59.55209136688317   MAE: 6.608117735497109   R^2: 0.09813081089169173
---- n features = 10
MSE: 59.59815916027962   MAE: 6.610330835548313   R^2: 0.0965567966100527
---- n features = 11
MSE: 59.55423347560355   MAE: 6.6078113652992005   R^2: 0.09862510424410273
---- n features = 12
MSE: 58.74496657365789   MAE: 6.5591529043803884   R^2: 0.11003598093494786
---- n features = 13
MSE: 58.591843133126375   MAE: 6.53474970219856   R^2: 0.11242201103751844
---- n features = 14
MSE: 56.94510841337241   MAE: 6.380222076912431   R^2: 0.13778987405804916
---- n features = 15
MSE: 56.60644595828394   MAE: 6.345803571493344   R^2: 0.14319586760485375
Optimal number of features:  15

Selected features:  age
Selected features:  Jitter(%)
Selected features:  Jitter(Abs)
Selected features:  Jitter:RAP
Selected features:  Jitter:DDP
Selected features:  Shimmer
Selected features:  Shimmer(dB)
Selected features:  Shimmer:APQ5
Selected features:  Shimmer:APQ11
Selected features:  Shimmer:DDA
Selected features:  HNR
Selected features:  RPDE
Selected features:  DFA
Selected features:  PPE
Selected features:  sex
Selected features:  ['x0' 'x1' 'x2' 'x3' 'x4' 'x5' 'x6' 'x7' 'x8' 'x9' 'x10' 'x11' 'x12' 'x13'
 'x14']
Model coefficients:  [[ 1.96519953e-01  4.36313941e+01 -6.28644125e+04 -3.69487912e+04
   1.24265425e+04  1.01730529e+02 -5.85832544e+00 -1.93038315e+02
   9.54677288e+01 -2.21953012e+01 -3.89430398e-01  7.68249643e-01
  -2.16521331e+01  1.88680948e+01 -1.21367667e+00]]
Model intercept:  [29.25034623]

from sklearn.feature_selection import SequentialFeatureSelector

def wrapper_selection(x,y, n_features):
    print("----- Optimal selection of number of features -----")
    n_feats = n_features

    mse_nfeat = []
    mae_nfeat = []
    r2_nfeat = []
    for n_feat in n_feats:
        print('---- n features =', n_feat)
        
        mse_cv = []
        mae_cv = []
        r2_cv = []

        kf = KFold(n_splits=5, shuffle = True)

        for train_index, test_index in kf.split(x):
        
            # Training phase
            x_train = x[train_index, :]
            y_train = y[train_index]     

            regr_cv = LinearRegression()

            
            fselection_cv = SequentialFeatureSelector(regr_cv, n_features_to_select = "auto")
            fselection_cv.fit(x_train, y_train)
            x_train = fselection_cv.transform(x_train)

            regr_cv.fit(x_train, y_train)

            # Test phase
            x_test = fselection_cv.transform(x[test_index, :])
            y_test = y[test_index]
            y_pred = regr_cv.predict(x_test)
        
            mse_i = mean_squared_error(y_test, y_pred)
            mse_cv.append(mse_i)
        
            mae_i = mean_absolute_error(y_test, y_pred)
            mae_cv.append(mae_i)

            r2_i = r2_score(y_test, y_pred)    
            r2_cv.append(r2_i)      
        

        mse = np.average(mse_cv)
        mse_nfeat.append(mse)
        
        mae = np.average(mae_cv)
        mae_nfeat.append(mae)
        
        r2 = np.average(r2_cv)
        r2_nfeat.append(r2)
        
        print('MSE:', mse, '  MAE:', mae,'  R^2:', r2)

    opt_index = np.argmin(mse_nfeat)
    opt_features = n_feats[opt_index]
    print("Optimal number of features: ", opt_features)

    fig, axs = plt.subplots(1, 3, tight_layout=True)
    axs[0].plot(n_feats, mse_nfeat)
    axs[0].set_xlabel("features")
    axs[0].set_ylabel("MSE")

    axs[1].plot(n_feats, mae_nfeat)
    axs[1].set_xlabel("features")
    axs[1].set_ylabel("MAE")

    axs[2].plot(n_feats, r2_nfeat)
    axs[2].set_xlabel("features")
    axs[2].set_ylabel("r^2")

    plt.show()

    return opt_features

X_np = df_X.to_numpy()
y_np = df_y.to_numpy().ravel()

n_features = list(range(1, X_np.shape[1] + 1))

opt_features = wrapper_selection(X_np, y_np, n_features)

# Fit model with optimal number of features
regr = LinearRegression()
fselection = SequentialFeatureSelector(regr, n_features_to_select = opt_features)
fselection.fit(X_np, y_np)

for i in range(len(fselection.get_support())): 
    if fselection.get_support()[i]:
        print("Selected features: ",df_X.columns[i])
print("Selected features: ", fselection.get_feature_names_out())

x_transformed = fselection.transform(X_np)
regr.fit(x_transformed, y)
print("Model coefficients: ", regr.coef_)
print("Model intercept: ", regr.intercept_)

----- Optimal selection of number of features -----
---- n features = 1
MSE: 58.88978716814447   MAE: 6.571484471403795   R^2: 0.10818635352885524
---- n features = 2
MSE: 59.21743429929476   MAE: 6.593539850588182   R^2: 0.1038060221217199
---- n features = 3
MSE: 59.200944871322555   MAE: 6.592100852614601   R^2: 0.102902468842249
---- n features = 4
MSE: 58.947546421458775   MAE: 6.576366108346706   R^2: 0.10737203034365024
---- n features = 5
MSE: 59.03190510803139   MAE: 6.576060823940002   R^2: 0.10597611799087339
---- n features = 6
MSE: 59.342975926425844   MAE: 6.6023096852367145   R^2: 0.10041193962339645
---- n features = 7
MSE: 59.25717467924771   MAE: 6.596511954625953   R^2: 0.10293243617229615
---- n features = 8
MSE: 59.01548686547053   MAE: 6.578862021061539   R^2: 0.10598285903063653
---- n features = 9
MSE: 59.070841449164746   MAE: 6.58402013811654   R^2: 0.10464404829430826
---- n features = 10
MSE: 59.18571072823181   MAE: 6.5804134859491485   R^2: 0.10369754828531938
---- n features = 11
MSE: 58.9641485247662   MAE: 6.5660277580089454   R^2: 0.10708435844475181
---- n features = 12
MSE: 59.377202033293656   MAE: 6.6028310828011625   R^2: 0.10000501031802025
---- n features = 13
MSE: 59.08116853640333   MAE: 6.596310207040114   R^2: 0.10543911242524495
---- n features = 14
MSE: 59.16417187310041   MAE: 6.590507792371767   R^2: 0.10384311462498375
---- n features = 15
MSE: 59.08778520386924   MAE: 6.581989684312167   R^2: 0.10566778388056455
Optimal number of features:  1

Selected features:  age
Selected features:  ['x0']
Model coefficients:  [[0.25218975]]
Model intercept:  [4.95308778]

from sklearn.feature_selection import RFE

def recursive_selection(x,y,n_features):
    print("----- Optimal selection of number of features -----")

    n_feats = n_features

    mse_nfeat = []
    mae_nfeat = []
    r2_nfeat = []
    for n_feat in n_feats:
        print('---- n features =', n_feat)
        
        mse_cv = []
        mae_cv = []
        r2_cv = []

        kf = KFold(n_splits=5, shuffle = True)

        for train_index, test_index in kf.split(x):
        
            # Training phase
            x_train = x[train_index, :]
            y_train = y[train_index]     

            regr_cv = LinearRegression()

            fselection_cv = RFE(regr_cv, n_features_to_select=n_feat)
            fselection_cv.fit(x_train, y_train)
            x_train = fselection_cv.transform(x_train)

            regr_cv.fit(x_train, y_train)

            # Test phase
            x_test = fselection_cv.transform(x[test_index, :])
            y_test = y[test_index]
            y_pred = regr_cv.predict(x_test)
        
            mse_i = mean_squared_error(y_test, y_pred)
            mse_cv.append(mse_i)
        
            mae_i = mean_absolute_error(y_test, y_pred)
            mae_cv.append(mae_i)

            r2_i = r2_score(y_test, y_pred)    
            r2_cv.append(r2_i)      
        

        mse = np.average(mse_cv)
        mse_nfeat.append(mse)
        
        mae = np.average(mae_cv)
        mae_nfeat.append(mae)
        
        r2 = np.average(r2_cv)
        r2_nfeat.append(r2)
        
        print('MSE:', mse, '  MAE:', mae,'  R^2:', r2)

    opt_index = np.argmin(mse_nfeat)
    opt_features = n_feats[opt_index]
    #print("Optimal number of features: ", opt_features)

    fig, axs = plt.subplots(1, 3, tight_layout=True)
    axs[0].plot(n_feats, mse_nfeat)
    axs[0].set_xlabel("features")
    axs[0].set_ylabel("MSE")

    axs[1].plot(n_feats, mae_nfeat)
    axs[1].set_xlabel("features")
    axs[1].set_ylabel("MAE")

    axs[2].plot(n_feats, r2_nfeat)
    axs[2].set_xlabel("features")
    axs[2].set_ylabel("r^2")

    plt.show()
    return opt_features

X_np = df_X.to_numpy()
y_np = df_y.to_numpy().ravel()

#Generando número de lista de características, no en rango
n_features = list(range(1, X.shape[1] + 1))

opt_features =recursive_selection(X_np, y_np, n_features)

# Fit model with optimal number of features
regr = LinearRegression()
fselection = RFE(regr, n_features_to_select = opt_features)
fselection.fit(X_np, y_np)

for i in range(len(fselection.support_)):
    if fselection.support_[i]:
        print("Selected features: ", X_np.columns[i])
print("Selected features: ", fselection.get_feature_names_out())

x_transformed = fselection.transform(X_np)
regr.fit(x_transformed, y)
print("Model coefficients: ", regr.coef_)
print("Model intercept: ", regr.intercept_)

----- Optimal selection of number of features -----
---- n features = 1
MSE: 65.75990526085835   MAE: 6.9504375732296255   R^2: 0.0038676653544396757
---- n features = 2
MSE: 65.7627590450476   MAE: 6.94906302811125   R^2: 0.0039726690530456745
---- n features = 3
MSE: 65.78426513791153   MAE: 6.951342021020844   R^2: 0.004229296423902973
---- n features = 4
MSE: 65.35472665270053   MAE: 6.941635647313044   R^2: 0.009310102400269171
---- n features = 5
MSE: 64.57067600937253   MAE: 6.864245886088801   R^2: 0.02122988780755184
---- n features = 6
MSE: 63.643578727597706   MAE: 6.810747505477023   R^2: 0.03620617666039041
---- n features = 7
MSE: 63.8409161379282   MAE: 6.811172910236327   R^2: 0.033227140575342526
---- n features = 8
MSE: 60.964382952828046   MAE: 6.642364744978326   R^2: 0.07638463095635088
---- n features = 9
MSE: 60.37651403624598   MAE: 6.594998752285181   R^2: 0.08555596406720942
---- n features = 10
MSE: 60.20274602360678   MAE: 6.586963824208683   R^2: 0.08749218520592013
---- n features = 11
MSE: 60.230518724743526   MAE: 6.574452857912428   R^2: 0.08688997424494208
---- n features = 12
MSE: 60.55063900367272   MAE: 6.564762286552866   R^2: 0.08188083972639268
---- n features = 13
MSE: 60.15327905270931   MAE: 6.53836688851635   R^2: 0.08951153989541014
---- n features = 14
MSE: 58.59641364938481   MAE: 6.468637466600922   R^2: 0.1118557342192068
---- n features = 15
MSE: 56.972009020696895   MAE: 6.356525952707213   R^2: 0.1367613147177548

Selected features:  age
Selected features:  Jitter(%)
Selected features:  Jitter(Abs)
Selected features:  Jitter:RAP
Selected features:  Jitter:DDP
Selected features:  Shimmer
Selected features:  Shimmer(dB)
Selected features:  Shimmer:APQ5
Selected features:  Shimmer:APQ11
Selected features:  Shimmer:DDA
Selected features:  HNR
Selected features:  RPDE
Selected features:  DFA
Selected features:  PPE
Selected features:  sex
Selected features:  ['x0' 'x1' 'x2' 'x3' 'x4' 'x5' 'x6' 'x7' 'x8' 'x9' 'x10' 'x11' 'x12' 'x13'
 'x14']
Model coefficients:  [[ 1.96519953e-01  4.36313941e+01 -6.28644125e+04 -3.69487912e+04
   1.24265425e+04  1.01730529e+02 -5.85832544e+00 -1.93038315e+02
   9.54677288e+01 -2.21953012e+01 -3.89430398e-01  7.68249643e-01
  -2.16521331e+01  1.88680948e+01 -1.21367667e+00]]
Model intercept:  [29.25034623]

from sklearn.feature_selection import SelectFromModel
from sklearn.neighbors import KNeighborsRegressor

def filter_selection_knn(x, y, n_features):
    print("----- Optimal selection of number of features -----")

    n_feats = n_features

    mse_nfeat = []
    mae_nfeat = []
    r2_nfeat = []
    for n_feat in n_feats:
        print('---- n features =', n_feat)
        
        mse_cv = []
        mae_cv = []
        r2_cv = []

        kf = KFold(n_splits=5, shuffle=True)

        for train_index, test_index in kf.split(x):
        
            # Training phase
            x_train = x[train_index, :]
            y_train = y[train_index]     
            
            fselection_cv = SelectKBest(f_regression, k=n_feat)
            fselection_cv.fit(x_train, y_train)
            x_train = fselection_cv.transform(x_train)

            regr_cv = KNeighborsRegressor(n_neighbors=5)
            regr_cv.fit(x_train, y_train)

            # Test phase
            x_test = fselection_cv.transform(x[test_index, :])
            y_test = y[test_index]
            y_pred = regr_cv.predict(x_test)
        
            mse_i = mean_squared_error(y_test, y_pred)
            mse_cv.append(mse_i)
        
            mae_i = mean_absolute_error(y_test, y_pred)
            mae_cv.append(mae_i)

            r2_i = r2_score(y_test, y_pred)    
            r2_cv.append(r2_i)      
        
        mse = np.average(mse_cv)
        mse_nfeat.append(mse)
        
        mae = np.average(mae_cv)
        mae_nfeat.append(mae)
        
        r2 = np.average(r2_cv)
        r2_nfeat.append(r2)
        
        print('MSE:', mse, '  MAE:', mae, '  R^2:', r2)

    opt_index = np.argmin(mse_nfeat)
    opt_features = n_feats[opt_index]
    print("Optimal number of features: ", opt_features)

    fig, axs = plt.subplots(1, 3, tight_layout=True)
    axs[0].plot(n_feats, mse_nfeat)
    axs[0].set_xlabel("k")
    axs[0].set_ylabel("MSE")

    axs[1].plot(n_feats, mae_nfeat)
    axs[1].set_xlabel("k")
    axs[1].set_ylabel("MAE")

    axs[2].plot(n_feats, r2_nfeat)
    axs[2].set_xlabel("k")
    axs[2].set_ylabel("r^2")

    plt.show()

    return opt_features

# Aplicación del modelo KNN con el número óptimo de características
X_np = df_X.to_numpy()
y_np = df_y.to_numpy().ravel()

n_features = list(range(1, X_np.shape[1] + 1))
opt_features = filter_selection_knn(X_np, y_np, n_features)

# Fit model with optimal number of features
regr = KNeighborsRegressor(n_neighbors=5)
fselection = SelectKBest(f_regression, k=opt_features)
fselection.fit(X_np, y_np)

for i in range(len(fselection.get_support())): 
    if fselection.get_support()[i]:
        print("Selected features: ", df_X.columns[i])
print("Selected features: ", fselection.get_feature_names_out())

x_transformed = fselection.transform(X_np)
regr.fit(x_transformed, y_np)

print("Modelo ajustado con las características seleccionadas.")

----- Optimal selection of number of features -----
---- n features = 1
MSE: 47.93807842612235   MAE: 4.777798161702128   R^2: 0.2735967853129878
---- n features = 2
MSE: 24.317699499472884   MAE: 3.50677354893617   R^2: 0.6317032420804723
---- n features = 3
MSE: 23.282341369713496   MAE: 3.4210451370212764   R^2: 0.6463645401014431
---- n features = 4
MSE: 22.95872415920218   MAE: 3.379794491914894   R^2: 0.6524647820588922
---- n features = 5
MSE: 20.60775102665954   MAE: 3.174437045106383   R^2: 0.6874300594915018
---- n features = 6
MSE: 18.354891491138588   MAE: 2.9453916119148933   R^2: 0.7211186073673168
---- n features = 7
MSE: 17.097514459804323   MAE: 2.8492717004255317   R^2: 0.7410684955355642
---- n features = 8
MSE: 17.201069747154587   MAE: 2.84826245787234   R^2: 0.7392401489934868
---- n features = 9
MSE: 17.122566662749485   MAE: 2.8548182365957446   R^2: 0.740553009056006
---- n features = 10
MSE: 17.156309153872748   MAE: 2.85737290893617   R^2: 0.740310524844151
---- n features = 11
MSE: 17.238215803810792   MAE: 2.862948272340426   R^2: 0.7389036020098807
---- n features = 12
MSE: 17.189599517977598   MAE: 2.858810471489362   R^2: 0.7395496162620218
---- n features = 13
MSE: 17.287837499832648   MAE: 2.8610996493617025   R^2: 0.7383011241615893
---- n features = 14
MSE: 17.514030856480474   MAE: 2.872266338723404   R^2: 0.7342532238273332
---- n features = 15
MSE: 9.707268928648306   MAE: 2.159997249361702   R^2: 0.8530000054101086
Optimal number of features:  15

Selected features:  age
Selected features:  Jitter(%)
Selected features:  Jitter(Abs)
Selected features:  Jitter:RAP
Selected features:  Jitter:DDP
Selected features:  Shimmer
Selected features:  Shimmer(dB)
Selected features:  Shimmer:APQ5
Selected features:  Shimmer:APQ11
Selected features:  Shimmer:DDA
Selected features:  HNR
Selected features:  RPDE
Selected features:  DFA
Selected features:  PPE
Selected features:  sex
Selected features:  ['x0' 'x1' 'x2' 'x3' 'x4' 'x5' 'x6' 'x7' 'x8' 'x9' 'x10' 'x11' 'x12' 'x13'
 'x14']
Modelo ajustado con las características seleccionadas.

def wrapper_selection_knn(x,y, n_features):
    print("----- Optimal selection of number of features -----")
    n_feats = n_features

    mse_nfeat = []
    mae_nfeat = []
    r2_nfeat = []
    for n_feat in n_feats:
        print('---- n features =', n_feat)
        
        mse_cv = []
        mae_cv = []
        r2_cv = []

        kf = KFold(n_splits=5, shuffle = True)

        for train_index, test_index in kf.split(x):
        
            # Training phase
            x_train = x[train_index, :]
            y_train = y[train_index]     

            regr_cv = KNeighborsRegressor(n_neighbors=5)

            
            fselection_cv = SequentialFeatureSelector(regr_cv, n_features_to_select = "auto")
            fselection_cv.fit(x_train, y_train)
            x_train = fselection_cv.transform(x_train)

            regr_cv.fit(x_train, y_train)

            # Test phase
            x_test = fselection_cv.transform(x[test_index, :])
            y_test = y[test_index]
            y_pred = regr_cv.predict(x_test)
        
            mse_i = mean_squared_error(y_test, y_pred)
            mse_cv.append(mse_i)
        
            mae_i = mean_absolute_error(y_test, y_pred)
            mae_cv.append(mae_i)

            r2_i = r2_score(y_test, y_pred)    
            r2_cv.append(r2_i)      
        

        mse = np.average(mse_cv)
        mse_nfeat.append(mse)
        
        mae = np.average(mae_cv)
        mae_nfeat.append(mae)
        
        r2 = np.average(r2_cv)
        r2_nfeat.append(r2)
        
        print('MSE:', mse, '  MAE:', mae,'  R^2:', r2)

    opt_index = np.argmin(mse_nfeat)
    opt_features = n_feats[opt_index]
    print("Optimal number of features: ", opt_features)

    fig, axs = plt.subplots(1, 3, tight_layout=True)
    axs[0].plot(n_feats, mse_nfeat)
    axs[0].set_xlabel("features")
    axs[0].set_ylabel("MSE")

    axs[1].plot(n_feats, mae_nfeat)
    axs[1].set_xlabel("features")
    axs[1].set_ylabel("MAE")

    axs[2].plot(n_feats, r2_nfeat)
    axs[2].set_xlabel("features")
    axs[2].set_ylabel("r^2")

    plt.show()

    return opt_features

X_np = df_X.to_numpy()
y_np = df_y.to_numpy().ravel()

n_features = list(range(1, X_np.shape[1] + 1))

opt_features = wrapper_selection(X_np, y_np, n_features)

# Fit model with optimal number of features
regr = KNeighborsRegressor(n_neighbors=5)
fselection = SequentialFeatureSelector(regr, n_features_to_select = opt_features)
fselection.fit(X_np, y_np)

for i in range(len(fselection.get_support())): 
    if fselection.get_support()[i]:
        print("Selected features: ",df_X.columns[i])
print("Selected features: ", fselection.get_feature_names_out())

x_transformed = fselection.transform(X_np)
regr.fit(x_transformed, y)

print("Modelo ajustado con las características seleccionadas.")

----- Optimal selection of number of features -----
---- n features = 1
MSE: 59.34760860100374   MAE: 6.595670610170674   R^2: 0.1013113187598083
---- n features = 2
MSE: 59.15797838057383   MAE: 6.584643462729472   R^2: 0.10412548607825049
---- n features = 3
MSE: 59.09706099599292   MAE: 6.590790209408409   R^2: 0.10442001820627171
---- n features = 4
MSE: 59.31629703268288   MAE: 6.595676643391144   R^2: 0.1021180059838904
---- n features = 5
MSE: 59.166585309002656   MAE: 6.589141758316506   R^2: 0.10320356138321247
---- n features = 6
MSE: 59.464386251312746   MAE: 6.599897948859976   R^2: 0.09929610664992088
---- n features = 7
MSE: 59.02223446636926   MAE: 6.580355751444176   R^2: 0.10575801198118387
---- n features = 8
MSE: 59.10332742000609   MAE: 6.585280306042774   R^2: 0.10308142063033432
---- n features = 9
MSE: 59.28310716865288   MAE: 6.5910971261368925   R^2: 0.10122552373044073
---- n features = 10
MSE: 59.01720172802909   MAE: 6.579123018445931   R^2: 0.10630569664291663
---- n features = 11
MSE: 59.00308066175184   MAE: 6.582890351040604   R^2: 0.10596869743874224
---- n features = 12
MSE: 59.1398125503031   MAE: 6.581044457169879   R^2: 0.10418662003865267
---- n features = 13
MSE: 59.195302361450715   MAE: 6.584658553594556   R^2: 0.10312350771069383
---- n features = 14
MSE: 59.04620017250011   MAE: 6.580068466063436   R^2: 0.10628383317910595
---- n features = 15
MSE: 59.14954859449473   MAE: 6.582543179231756   R^2: 0.10348200920827337
Optimal number of features:  11

Selected features:  age
Selected features:  Jitter(%)
Selected features:  Jitter(Abs)
Selected features:  Jitter:RAP
Selected features:  Shimmer
Selected features:  Shimmer(dB)
Selected features:  Shimmer:APQ5
Selected features:  Shimmer:APQ11
Selected features:  Shimmer:DDA
Selected features:  DFA
Selected features:  sex
Selected features:  ['x0' 'x1' 'x2' 'x3' 'x5' 'x6' 'x7' 'x8' 'x9' 'x12' 'x14']
Modelo ajustado con las características seleccionadas.

def filter_selection_knn(x, y, n_features):
    print("----- Optimal selection of number of features -----")

    mse_nfeat = []
    mae_nfeat = []
    r2_nfeat = []
    for n_feat in n_features:
        print('---- n features =', n_feat)
        
        mse_cv = []
        mae_cv = []
        r2_cv = []

        kf = KFold(n_splits=5, shuffle=True)

        for train_index, test_index in kf.split(x):
        
            # Training phase
            x_train = x[train_index, :]
            y_train = y[train_index]     

            # Selección de características usando SelectKBest con f_regression
            fselection_cv = SelectKBest(score_func=f_regression, k=n_feat)
            x_train = fselection_cv.fit_transform(x_train, y_train)

            regr_cv = KNeighborsRegressor(n_neighbors=5)
            regr_cv.fit(x_train, y_train)

            # Test phase
            x_test = fselection_cv.transform(x[test_index, :])
            y_test = y[test_index]
            y_pred = regr_cv.predict(x_test)
        
            mse_i = mean_squared_error(y_test, y_pred)
            mse_cv.append(mse_i)
        
            mae_i = mean_absolute_error(y_test, y_pred)
            mae_cv.append(mae_i)

            r2_i = r2_score(y_test, y_pred)    
            r2_cv.append(r2_i)      

        mse = np.average(mse_cv)
        mse_nfeat.append(mse)
        
        mae = np.average(mae_cv)
        mae_nfeat.append(mae)
        
        r2 = np.average(r2_cv)
        r2_nfeat.append(r2)
        
        print('MSE:', mse, '  MAE:', mae,'  R^2:', r2)

    opt_index = np.argmin(mse_nfeat)
    opt_features = n_features[opt_index]
    print("Optimal number of features: ", opt_features)

    fig, axs = plt.subplots(1, 3, tight_layout=True)
    axs[0].plot(n_features, mse_nfeat)
    axs[0].set_xlabel("k")
    axs[0].set_ylabel("MSE")

    axs[1].plot(n_features, mae_nfeat)
    axs[1].set_xlabel("k")
    axs[1].set_ylabel("MAE")

    axs[2].plot(n_features, r2_nfeat)
    axs[2].set_xlabel("k")
    axs[2].set_ylabel("r^2")

    plt.show()

    return opt_features

X_np = df_X.to_numpy()
y_np = df_y.to_numpy().ravel()

# Generando lista de número de características
n_features = list(range(1, X_np.shape[1] + 1))

# Obtener el número óptimo de características
opt_features = filter_selection_knn(X_np, y_np, n_features)

# Ajustar el modelo con el número óptimo de características
regr = KNeighborsRegressor(n_neighbors=5)
fselection = SelectKBest(score_func=f_regression, k=opt_features)
X_selected = fselection.fit_transform(X_np, y_np)

selected_features = df_X.columns[fselection.get_support()]
print("Selected features: ", selected_features)

regr.fit(X_selected, y_np)
print("Modelo ajustado con las características seleccionadas.")

----- Optimal selection of number of features -----
---- n features = 1
MSE: 47.04745162546417   MAE: 4.654235530212765   R^2: 0.28752017226450155
---- n features = 2
MSE: 25.244382466858482   MAE: 3.5689276051063827   R^2: 0.6172346133247337
---- n features = 3
MSE: 23.45651618999973   MAE: 3.4018965548936166   R^2: 0.6451133874608497
---- n features = 4
MSE: 23.260926520008915   MAE: 3.402694491914893   R^2: 0.6473635873043969
---- n features = 5
MSE: 20.926808299485074   MAE: 3.1923297531914896   R^2: 0.6830628390320189
---- n features = 6
MSE: 19.17933259698608   MAE: 3.0205230672340426   R^2: 0.7095325962528832
---- n features = 7
MSE: 18.030087376365888   MAE: 2.9308562042553192   R^2: 0.7271313714722586
---- n features = 8
MSE: 17.333891637300628   MAE: 2.8638473429787235   R^2: 0.7367862848562116
---- n features = 9
MSE: 17.036761498613107   MAE: 2.848948493617021   R^2: 0.7414572717506436
---- n features = 10
MSE: 16.944562390053513   MAE: 2.8317771812765957   R^2: 0.743028327628474
---- n features = 11
MSE: 17.461273044445548   MAE: 2.8686014638297874   R^2: 0.7353195181542412
---- n features = 12
MSE: 17.22832822432967   MAE: 2.856582114042553   R^2: 0.7390647084209288
---- n features = 13
MSE: 17.347280308662604   MAE: 2.8609842723404255   R^2: 0.7373116935038795
---- n features = 14
MSE: 17.32118724038829   MAE: 2.8580348765957444   R^2: 0.7374328247303565
---- n features = 15
MSE: 9.66387328762914   MAE: 2.1650288714893615   R^2: 0.8537447610536585
Optimal number of features:  15

Selected features:  Index(['age', 'Jitter(%)', 'Jitter(Abs)', 'Jitter:RAP', 'Jitter:DDP',
       'Shimmer', 'Shimmer(dB)', 'Shimmer:APQ5', 'Shimmer:APQ11',
       'Shimmer:DDA', 'HNR', 'RPDE', 'DFA', 'PPE', 'sex'],
      dtype='object')
Modelo ajustado con las características seleccionadas.

from sklearn.svm import SVR
def cross_validate_model(model, X, y, cv_folds=5, scoring='neg_mean_squared_error'):

    if isinstance(model, SVR):
        model = make_pipeline(StandardScaler(), model)
    
    kf = KFold(n_splits=cv_folds, shuffle=True, random_state=42)
    
    scores = cross_val_score(model, X, y, cv=kf, scoring=scoring)
    
    mean_score = scores.mean()
    
    return mean_score

def filter_selection(X, y, model, k_features=5):

    selector = SelectKBest(score_func=f_regression, k=k_features)
    pipeline = make_pipeline(StandardScaler(), selector, model)
    
    mean_score = cross_validate_model(pipeline, X, y, cv_folds=5, scoring='neg_mean_squared_error')

    selector.fit(X, y)
    selected_features = selector.get_support(indices=True)
    
    return mean_score, selected_features

def wrapper_selection(X, y, model, k_features=5):

    sfs = SequentialFeatureSelector(model, n_features_to_select=k_features, direction='forward')
    pipeline = make_pipeline(StandardScaler(), sfs, model)
    
    mean_score = cross_validate_model(pipeline, X, y, cv_folds=5, scoring='neg_mean_squared_error')
    
    sfs.fit(X, y)
    selected_features = sfs.get_support(indices=True)
    
    return mean_score, selected_features

from sklearn.neighbors import KNeighborsClassifier

def recursive_selection(X, y, model, k_features=5):

    if isinstance(model, (SVR, KNeighborsClassifier)):
        raise ValueError("RFE no es compatible con el modelo seleccionado. Usa un estimador que tenga coef_ o feature_importances_")
    
    rfe = RFE(model, n_features_to_select=k_features)
    pipeline = make_pipeline(StandardScaler(), rfe, model)
    
    mean_score = cross_validate_model(pipeline, X, y, cv_folds=5, scoring='neg_mean_squared_error')
    
    rfe.fit(X, y)
    selected_features = rfe.get_support(indices=True)
    
    return mean_score, selected_features

import numpy as np
from sklearn.tree import DecisionTreeRegressor
from sklearn.ensemble import RandomForestRegressor
from sklearn.neural_network import MLPRegressor
from sklearn.neighbors import KNeighborsClassifier

X = df_X.to_numpy()
y = df_y.to_numpy().ravel()

# Modelos a evaluar
models = {
    'Máquinas de Vectores de Soporte (SVR)': SVR(kernel='rbf'),
    'DecisionTreeRegressor': DecisionTreeRegressor(),
    'RandomForestRegressor': RandomForestRegressor(),
    'MLPRegressor': MLPRegressor(hidden_layer_sizes=(100,), activation='relu', max_iter=1000)
}


for name, model in models.items():
    print(f"\n\nEvaluando modelo: {name}")
    
    # Método Filter
    print("Método Filter")
    mean_score, selected_features = filter_selection(X, y, model)
    print(f"Error cuadrático medio: {-mean_score:.3f}")
    print(f"Número de características seleccionadas: {len(selected_features)}")
    print(f"Índices de características seleccionadas: {selected_features}")
    
    # Método Wrapper
    print("Método Wrapper")
    mean_score, selected_features = wrapper_selection(X, y, model)
    print(f"Error cuadrático medio: {-mean_score:.3f}")
    print(f"Número de características seleccionadas: {len(selected_features)}")
    print(f"Índices de características seleccionadas: {selected_features}")
    
    # Método Recursivo
    print("Método Recursivo")
    if isinstance(model, (SVR, KNeighborsClassifier)):
        print("El modelo no es compatible con RFE.")
    else:
        mean_score, selected_features = recursive_selection(X, y, model)
        print(f"Error cuadrático medio: {-mean_score:.3f}")
        print(f"Número de características seleccionadas: {len(selected_features)}")
        print(f"Índices de características seleccionadas: {selected_features}")
    
    print("\n")


Evaluando modelo: Máquinas de Vectores de Soporte (SVR)
Método Filter
Error cuadrático medio: 47.852
Número de características seleccionadas: 5
Índices de características seleccionadas: [ 0  8 10 11 13]
Método Wrapper
Error cuadrático medio: 56.060
Número de características seleccionadas: 5
Índices de características seleccionadas: [ 1  3  4 13 14]
Método Recursivo
El modelo no es compatible con RFE.


Evaluando modelo: DecisionTreeRegressor
Método Filter
Error cuadrático medio: 27.486
Número de características seleccionadas: 5
Índices de características seleccionadas: [ 0  8 10 11 13]
Método Wrapper
Error cuadrático medio: 15.180
Número de características seleccionadas: 5
Índices de características seleccionadas: [ 0  2 10 13 14]
Método Recursivo
Error cuadrático medio: 12.140
Número de características seleccionadas: 5
Índices de características seleccionadas: [ 0  2  9 12 14]


Evaluando modelo: RandomForestRegressor
Método Filter
Error cuadrático medio: 15.497
Número de características seleccionadas: 5
Índices de características seleccionadas: [ 0  8 10 11 13]
Método Wrapper
Error cuadrático medio: 39.804
Número de características seleccionadas: 5
Índices de características seleccionadas: [ 1  2  8 13 14]
Método Recursivo
Error cuadrático medio: 7.002
Número de características seleccionadas: 5
Índices de características seleccionadas: [ 0  2  9 12 14]


Evaluando modelo: MLPRegressor
Método Filter

c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(

Error cuadrático medio: 41.087
Número de características seleccionadas: 5
Índices de características seleccionadas: [ 0  8 10 11 13]
Método Wrapper

c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:690: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
c:\Users\palmi\.conda\envs\concentracion\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:697: UserWarning: Training interrupted by user.
  warnings.warn("Training interrupted by user.")

	Country	Year	Status	Life expectancy	Adult Mortality	infant deaths	Alcohol	percentage expenditure	Hepatitis B	Measles	...	Polio	Total expenditure	Diphtheria	HIV/AIDS	GDP	Population	thinness 1-19 years	thinness 5-9 years	Income composition of resources	Schooling
0	Afghanistan	2015	Developing	65.0	263.0	62	0.01	71.279624	65.0	1154	...	6.0	8.16	65.0	0.1	584.259210	33736494.0	17.2	17.3	0.479	10.1
1	Afghanistan	2014	Developing	59.9	271.0	64	0.01	73.523582	62.0	492	...	58.0	8.18	62.0	0.1	612.696514	327582.0	17.5	17.5	0.476	10.0
2	Afghanistan	2013	Developing	59.9	268.0	66	0.01	73.219243	64.0	430	...	62.0	8.13	64.0	0.1	631.744976	31731688.0	17.7	17.7	0.470	9.9
3	Afghanistan	2012	Developing	59.5	272.0	69	0.01	78.184215	67.0	2787	...	67.0	8.52	67.0	0.1	669.959000	3696958.0	17.9	18.0	0.463	9.8
4	Afghanistan	2011	Developing	59.2	275.0	71	0.01	7.097109	68.0	3013	...	68.0	7.87	68.0	0.1	63.537231	2978599.0	18.2	18.2	0.454	9.5
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2933	Zimbabwe	2004	Developing	44.3	723.0	27	4.36	0.000000	68.0	31	...	67.0	7.13	65.0	33.6	454.366654	12777511.0	9.4	9.4	0.407	9.2
2934	Zimbabwe	2003	Developing	44.5	715.0	26	4.06	0.000000	7.0	998	...	7.0	6.52	68.0	36.7	453.351155	12633897.0	9.8	9.9	0.418	9.5
2935	Zimbabwe	2002	Developing	44.8	73.0	25	4.43	0.000000	73.0	304	...	73.0	6.53	71.0	39.8	57.348340	125525.0	1.2	1.3	0.427	10.0
2936	Zimbabwe	2001	Developing	45.3	686.0	25	1.72	0.000000	76.0	529	...	76.0	6.16	75.0	42.1	548.587312	12366165.0	1.6	1.7	0.427	9.8
2937	Zimbabwe	2000	Developing	46.0	665.0	24	1.68	0.000000	79.0	1483	...	78.0	7.10	78.0	43.5	547.358878	12222251.0	11.0	11.2	0.434	9.8

	Life expectancy	Adult Mortality	infant deaths	Alcohol	Hepatitis B	Measles	BMI	Polio	Total expenditure	Diphtheria	GDP	Population	thinness 1-19 years	Income composition of resources	Schooling
0	65.0	263.0	62	0.01	65.0	1154	19.1	6.0	8.16	65.0	584.259210	33736494.0	17.2	0.479	10.1
1	59.9	271.0	64	0.01	62.0	492	18.6	58.0	8.18	62.0	612.696514	327582.0	17.5	0.476	10.0
2	59.9	268.0	66	0.01	64.0	430	18.1	62.0	8.13	64.0	631.744976	31731688.0	17.7	0.470	9.9
3	59.5	272.0	69	0.01	67.0	2787	17.6	67.0	8.52	67.0	669.959000	3696958.0	17.9	0.463	9.8
4	59.2	275.0	71	0.01	68.0	3013	17.2	68.0	7.87	68.0	63.537231	2978599.0	18.2	0.454	9.5
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2933	44.3	723.0	27	4.36	68.0	31	27.1	67.0	7.13	65.0	454.366654	12777511.0	9.4	0.407	9.2
2934	44.5	715.0	26	4.06	7.0	998	26.7	7.0	6.52	68.0	453.351155	12633897.0	9.8	0.418	9.5
2935	44.8	73.0	25	4.43	73.0	304	26.3	73.0	6.53	71.0	57.348340	125525.0	1.2	0.427	10.0
2936	45.3	686.0	25	1.72	76.0	529	25.9	76.0	6.16	75.0	548.587312	12366165.0	1.6	0.427	9.8
2937	46.0	665.0	24	1.68	79.0	1483	25.5	78.0	7.10	78.0	547.358878	12222251.0	11.0	0.434	9.8

	Life expectancy	Adult Mortality	infant deaths	Alcohol	Hepatitis B	Measles	BMI	Polio	Total expenditure	Diphtheria	GDP	Population	thinness 1-19 years	Income composition of resources	Schooling
count	2928.000000	2928.000000	2938.000000	2744.000000	2385.000000	2938.000000	2904.000000	2919.000000	2712.00000	2919.000000	2490.000000	2.286000e+03	2904.000000	2771.000000	2775.000000
mean	69.224932	164.796448	30.303948	4.602861	80.940461	2419.592240	38.321247	82.550188	5.93819	82.324084	7483.158469	1.275338e+07	4.839704	0.627551	11.992793
std	9.523867	124.292079	117.926501	4.052413	25.070016	11467.272489	20.044034	23.428046	2.49832	23.716912	14270.169342	6.101210e+07	4.420195	0.210904	3.358920
min	36.300000	1.000000	0.000000	0.010000	1.000000	0.000000	1.000000	3.000000	0.37000	2.000000	1.681350	3.400000e+01	0.100000	0.000000	0.000000
25%	63.100000	74.000000	0.000000	0.877500	77.000000	0.000000	19.300000	78.000000	4.26000	78.000000	463.935626	1.957932e+05	1.600000	0.493000	10.100000
50%	72.100000	144.000000	3.000000	3.755000	92.000000	17.000000	43.500000	93.000000	5.75500	93.000000	1766.947595	1.386542e+06	3.300000	0.677000	12.300000
75%	75.700000	228.000000	22.000000	7.702500	97.000000	360.250000	56.200000	97.000000	7.49250	97.000000	5910.806335	7.420359e+06	7.200000	0.779000	14.300000
max	89.000000	723.000000	1800.000000	17.870000	99.000000	212183.000000	87.300000	99.000000	17.60000	99.000000	119172.741800	1.293859e+09	27.700000	0.948000	20.700000

	Life expectancy	Adult Mortality	infant deaths	Alcohol	Hepatitis B	Measles	BMI	Polio	Total expenditure	Diphtheria	GDP	Population	thinness 1-19 years	Income composition of resources	Schooling
32	75.6	19.0	21	NaN	95.0	63	59.5	95.0	NaN	95.0	4132.762920	39871528.0	6.0	0.743	14.4
44	71.7	146.0	20	0.34	NaN	15374	47.0	87.0	3.60	87.0	294.335560	3243514.0	6.3	0.663	11.5
45	71.6	145.0	20	0.36	NaN	5862	46.1	86.0	3.73	86.0	1774.336730	3199546.0	6.3	0.653	11.1
46	71.4	145.0	20	0.23	NaN	2686	45.3	89.0	3.84	89.0	1732.857979	31592153.0	6.4	0.644	10.9
47	71.3	145.0	21	0.25	NaN	0	44.4	86.0	3.49	86.0	1757.177970	3118366.0	6.5	0.636	10.7
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2918	46.4	64.0	39	2.33	NaN	881	17.6	85.0	8.18	83.0	429.158343	11421984.0	7.3	0.443	10.2
2919	45.5	69.0	41	2.44	NaN	25036	17.3	85.0	6.93	84.0	377.135244	111249.0	7.4	0.433	10.0
2920	44.6	611.0	43	2.61	NaN	16997	17.1	86.0	6.56	85.0	378.273624	1824125.0	7.4	0.424	9.8
2921	43.8	614.0	44	2.62	NaN	30930	16.8	85.0	7.16	85.0	341.955625	1531221.0	7.5	0.418	9.6
2922	67.0	336.0	22	NaN	87.0	0	31.8	88.0	NaN	87.0	118.693830	15777451.0	5.6	0.507	10.3

	Life expectancy	Adult Mortality	infant deaths	Alcohol	Hepatitis B	Measles	BMI	Polio	Total expenditure	Diphtheria	GDP	Population	thinness 1-19 years	Income composition of resources	Schooling
0	65.0	263.0	62	0.01	65.0	1154	19.1	6.0	8.16	65.0	584.259210	33736494.0	17.2	0.479	10.1
1	59.9	271.0	64	0.01	62.0	492	18.6	58.0	8.18	62.0	612.696514	327582.0	17.5	0.476	10.0
2	59.9	268.0	66	0.01	64.0	430	18.1	62.0	8.13	64.0	631.744976	31731688.0	17.7	0.470	9.9
3	59.5	272.0	69	0.01	67.0	2787	17.6	67.0	8.52	67.0	669.959000	3696958.0	17.9	0.463	9.8
4	59.2	275.0	71	0.01	68.0	3013	17.2	68.0	7.87	68.0	63.537231	2978599.0	18.2	0.454	9.5
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2933	44.3	723.0	27	4.36	68.0	31	27.1	67.0	7.13	65.0	454.366654	12777511.0	9.4	0.407	9.2
2934	44.5	715.0	26	4.06	7.0	998	26.7	7.0	6.52	68.0	453.351155	12633897.0	9.8	0.418	9.5
2935	44.8	73.0	25	4.43	73.0	304	26.3	73.0	6.53	71.0	57.348340	125525.0	1.2	0.427	10.0
2936	45.3	686.0	25	1.72	76.0	529	25.9	76.0	6.16	75.0	548.587312	12366165.0	1.6	0.427	9.8
2937	46.0	665.0	24	1.68	79.0	1483	25.5	78.0	7.10	78.0	547.358878	12222251.0	11.0	0.434	9.8

	Adult Mortality^2	infant deaths^2	Alcohol^2	Hepatitis B^2	Measles ^2	BMI ^2	Polio^2	Total expenditure^2	Diphtheria ^2	GDP^2	...	Measles ^2	BMI ^2	Polio^2	Total expenditure^2	Diphtheria ^2	GDP^2	Population^2	thinness 1-19 years^2	Income composition of resources^2	Schooling^2
0	69169.0	3844	0.0001	4225.0	1331716	364.81	36.0	66.5856	4225.0	341358.824470	...	1331716	364.81	36.0	66.5856	4225.0	341358.824470	1.138151e+15	295.84	0.229441	102.01
1	73441.0	4096	0.0001	3844.0	242064	345.96	3364.0	66.9124	3844.0	375397.018268	...	242064	345.96	3364.0	66.9124	3844.0	375397.018268	1.073100e+11	306.25	0.226576	100.00
2	71824.0	4356	0.0001	4096.0	184900	327.61	3844.0	66.0969	4096.0	399101.714701	...	184900	327.61	3844.0	66.0969	4096.0	399101.714701	1.006900e+15	313.29	0.220900	98.01
3	73984.0	4761	0.0001	4489.0	7767369	309.76	4489.0	72.5904	4489.0	448845.061681	...	7767369	309.76	4489.0	72.5904	4489.0	448845.061681	1.366750e+13	320.41	0.214369	96.04
4	75625.0	5041	0.0001	4624.0	9078169	295.84	4624.0	61.9369	4624.0	4036.979723	...	9078169	295.84	4624.0	61.9369	4624.0	4036.979723	8.872052e+12	331.24	0.206116	90.25

	motor_UPDRS
0	28.199
1	28.447
2	28.695
3	28.905
4	29.187
...	...
5870	22.485
5871	21.988
5872	21.495
5873	21.007
5874	20.513

	age	Jitter(%)	Jitter(Abs)	Jitter:RAP	Jitter:DDP	Shimmer	Shimmer(dB)	Shimmer:APQ5	Shimmer:APQ11	Shimmer:DDA	HNR	RPDE	DFA	PPE	sex
0	72	0.00662	0.000034	0.00401	0.01204	0.02565	0.230	0.01309	0.01662	0.04314	21.640	0.41888	0.54842	0.16006	0
1	72	0.00300	0.000017	0.00132	0.00395	0.02024	0.179	0.01072	0.01689	0.02982	27.183	0.43493	0.56477	0.10810	0
2	72	0.00481	0.000025	0.00205	0.00616	0.01675	0.181	0.00844	0.01458	0.02202	23.047	0.46222	0.54405	0.21014	0
3	72	0.00528	0.000027	0.00191	0.00573	0.02309	0.327	0.01265	0.01963	0.03317	24.445	0.48730	0.57794	0.33277	0
4	72	0.00335	0.000020	0.00093	0.00278	0.01703	0.176	0.00929	0.01819	0.02036	26.126	0.47188	0.56122	0.19361	0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
5870	61	0.00406	0.000031	0.00167	0.00500	0.01896	0.160	0.01133	0.01549	0.02920	22.369	0.64215	0.55314	0.21367	0
5871	61	0.00297	0.000025	0.00119	0.00358	0.02315	0.215	0.01277	0.01904	0.03157	22.886	0.52598	0.56518	0.12621	0
5872	61	0.00349	0.000025	0.00152	0.00456	0.02499	0.244	0.01456	0.01877	0.04112	25.065	0.47792	0.57888	0.14157	0
5873	61	0.00281	0.000020	0.00128	0.00383	0.01484	0.131	0.00870	0.01307	0.02078	24.422	0.56865	0.56327	0.14204	0
5874	61	0.00282	0.000021	0.00135	0.00406	0.01907	0.171	0.01154	0.01470	0.02839	23.259	0.58608	0.57077	0.15336	0

Problemas de Regresión¶

Carlos Adrián Palmieri Álvarez - A01635776¶

Life Expectancy¶

1.Grafica cada variable predictora vs la variable de respuesta asignadas a tu número de matrícula.¶

2.Implementa la fórmula directa para calcular los coeficientes de un modelo de regresión lineal, y obtenga con ella el modelo que corresponde a la variable de respuesta y las variables predictoras asignadas a tu número de matrícula.¶

3. Evalúa con validación cruzada de k-pliegues tu modelo, calculando los valores de R2, MSE y MAE.¶

4. Utiliza validación cruzada de Monte Carlo con 1000 iteraciones para encontrar histogramas de R2, MSE y MAE.¶

5. Utiliza el método de validación cruzada asignado a tu matrícula para mostrar los histogramas de MSE y MAE. ¿Los histogramas son distintos a los obtenidos con el método de Monte Carlo?¶

Método de validación Leave-P-Out(LpOCV) para P = 2¶

Método de validación Leave One Out (LOOCV)¶

Histogramas¶

6. Agrega al conjunto de datos columnas que representen los cuadrados de las variables predictoras (por ejemplo, X112, X132), así como los productos entre pares de variables (por ejemplo, X1xX2, X3xX4). Repita los pasos 1, 2 y 3 pero con este nuevo conjunto de datos.¶

7. Implementa regresión Ridge con descenso de gradiente, y genera el gráfico de Ridge para el conjunto de datos original (sin las variables elevadas al cuadrado).¶

8. Utiliza una librería para generar el gráfico de Lasso para el conjunto de datos original (sin las variables elevadas al cuadrado). ¿Qué variables son más relevantes para el modelo?¶

9.Viendo los resultados de regresión, desarrolla una conclusión sobre los siguientes puntos:¶

A. ¿Consideras que el modelo de regresión lineal es efectivo para modelar los datos del problema? ¿Por qué?¶

B. ¿Observas una variabilidad importante en los valores de R2, MSE y MAE cuando aplicas validación cruzada? Detalla tu respuesta.¶

C. ¿Qué modelo es mejor para los datos del problema, el lineal o el cuadrático? ¿Por qué?¶

D.¿Qué variables son más relevantes para el modelo según Ridge y Lasso?¶

E. ¿Encuentras alguna relación interesante entre la variable de respuesta y los predictores?¶

Seguimiento Telemétrico de la Enfermedad de Parkinson¶

1. Evalúa con validación cruzada un modelo de regresión lineal para las variables asignadas según tu matrícula utilizando alguna librería o framework.¶

2. Encuentra el número óptimo de predictores para el modelo utilizando el método filter y validación cruzada. Una vez que tengas el número óptimo, muestra las características seleccionadas.¶

Método Filter¶

3,Repite el paso anterior pero con selección de características secuencial (Wrapper). Reporta los predictores óptimos encontrados por el método.¶

Método Wrapper¶

4.Haz el mismo proceso del paso 2, pero ahora con el método de selección de características recursivo. Reporta los predictores óptimos encontrados por el método.¶

Método Recursivo¶

5.Repita los pasos anteriores, pero utilizando un modelo de regresión no lineal como K-vecinos más cercanos.¶

Método Filter¶

Método Wrapper¶

Método Recursivo¶

6.Busca al menos otros 4 modelos de regresión no lineal, y lleva a cabo los pasos del 1 al 5.¶

Función cross_validate_model¶

Función método Filter¶

Función método Wrapper¶

Función método Recursivo¶

"Main"¶

7. Viendo los resultados de este ejercicio, escriba una conclusión sobre los siguientes puntos:¶

A. ¿Consideras que el modelo de regresión lineal es adecuado para los datos. ¿Por qué?¶

B. ¿Qué método de selección de características consideras que funciona bien con los datos? ¿Por qué?¶

C. Del proceso de selección de características, ¿puedes identificar algunas que sean sobresalientes? ¿Qué información relevantes observas de dichas características?¶

D. ¿Los modelos de regresión no lineal funcionaron mejor que el lineal? ¿Por qué?¶

E. ¿Se puede concluir algo interesante sobre los resultados de modelar estos datos con regresión? Argumenta tu respuesta.¶